Exhibit 3.11

AMENDED AND RESTATED

LIMITED LIABILITY COMPANY AGREEMENT

OF

SABINE PASS LNG-LP, LLC

A Delaware Limited Liability Company

This Amended and Restated Limited Liability Company Agreement (herein called the “Agreement”) of Sabine Pass LNG-LP, LLC, dated effective as of this 17^th day of August 2005, is (a) adopted by the Managers (as defined below) and (b) executed and agreed to, for good and valuable consideration, by the Member (as defined below).

ARTICLE I

DEFINITIONS

1.1. Definitions. The following terms used in this Agreement shall have the following meanings (unless otherwise expressly provided herein):

“Act” means the Delaware Limited Liability Company Act, as the same may be amended from time to time.

“Agreement” means this Agreement of the Company, as originally adopted and as amended from time to time.

“Business Day” means a day other than a Saturday, Sunday or other day which is a nationally recognized holiday in the United States of America.

“Capital Contribution” means any contribution to the capital of the Company in cash or property by the Member whenever made.

“Certificate” means the Certificate of Formation of the Company as filed with the Secretary of State of Delaware, as it shall be amended from time to time.

“Code” means the Internal Revenue Code of 1986, as amended. Any reference to a section of the Code shall include a reference to any amendatory or successor provision thereto.

“Company” means Sabine Pass LNG-LP, LLC, a Delaware limited liability company.

“Fiscal Year” means the Company’s fiscal year, which shall be the calendar year.

“Initial Capital Contribution” means the initial contribution to the capital of the Company made by the Member pursuant to this Agreement.

“Majority” means, with respect to any referenced group of Managers, a combination of any such Managers constituting more than fifty percent (50%) of the number of Managers of such referenced group who are then elected and qualified.

“Manager” means those Persons identified on Exhibit A or any other Persons who succeed such Persons in that capacity or are elected to act as additional managers of the Company as provided herein.

“Member” means Cheniere LNG Holdings, LLC, a Delaware limited liability company, and any Person hereafter admitted to the Company as a Member as provided in this Agreement, but does not include any Person who has ceased to be a Member in the Company.

“Membership Interest” means, with respect to the Member at anytime, the ownership interest of the Member at that time, which shall include all Units then owned thereby.

“Person” means any natural person, partnership, limited liability company, corporation, trust or other legal entity.

“Units” means units of ownership interest in the Company.

1.2. Other Definitional Provisions. All terms used in this Agreement that are not defined in this Article I have the meanings contained elsewhere in this Agreement.

ARTICLE II

FORMATION

2.1. Name and Formation. The name of the Company is Sabine Pass LNG-LP, LLC. The Company was formed as a limited liability company upon the filing of the Certificate pursuant to the Act.

2.2. Principal Place of Business. The principal place of business of the Company shall be at 2215-B Renaissance Drive, Suite 5, Las Vegas, NV 89119. The Company may locate its place(s) of business and registered office at any other place or places as the Member may from time to time deem necessary or advisable.

2.3. Registered Office and Agent. The registered office of the Company shall be at 2711 Centerville Road, Suite 400, Wilmington, Delaware 19808, and the name of its initial registered agent at such address shall be Corporation Service Company.

2.4. Duration. The period of duration of the Company is perpetual from the date its Certificate was filed with the Secretary of State of Delaware, unless the Company is earlier dissolved in accordance with either the provisions of this Agreement or the Act.

2.5. Purposes and Powers. The purpose for which the Company is organized is to transact any or all lawful business for which limited liability companies may be organized under the Act with the exception of the business of granting policies of insurance, or assuming insurance risks or banking as defined in Section 126 of Title 8 of the Delaware Code Annotated. The Company shall have the power to do any and all acts and things necessary, appropriate, proper, advisable, incidental to or convenient for the furtherance and accomplishment of such purposes, and for the protection and benefit of its business.

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2.6. Limitation of Liability. The liability of each Member and each employee of the Company to third parties for obligations of the Company shall be limited to the fullest extent provided in the Act and other applicable law.

ARTICLE III

RIGHTS AND DUTIES OF MANAGERS

3.1. Management. The powers of the Company shall be exercised by or under the authority of, and the business and affairs of the Company shall be managed under, its designated Manager or Managers. In addition to the powers and authorities expressly conferred by this Agreement upon the Managers, the Managers may exercise all such powers of the Company and do all such lawful acts and things as are not directed or required to be exercised or done by the Member by the Act, the Certificate or this Agreement, including, but not limited to, contracting for or incurring debts, liabilities and other obligations on behalf of the Company.

3.2. Number and Qualifications. The number of Managers shall not be less than one (1) nor more than seven (7) as may be determined by the Member from time to time, but no decrease in the number of Managers shall have the effect of shortening the term of any incumbent Manager. Managers need not be residents of the State of Delaware. The Managers in their discretion may elect from among the Managers a chairman of the Managers who shall preside at meetings of the Managers.

3.3. Election. At the first annual meeting of the Member and at each annual meeting thereafter, the Member shall elect one or more Managers to hold office until the next succeeding annual meeting. Unless removed in accordance with this Agreement, each Manager shall hold office for the term for which such person is elected and until such person’s successor shall be elected and qualified.

3.4. Vacancy. Any vacancy occurring for any reason in the number of Managers shall be filled by the Member. A Manager elected to fill a vacancy shall be elected for the unexpired term of the predecessor in office.

3.5. Removal. At a meeting called expressly for such purpose, all or any lesser number of Managers may be removed at any time, with or without cause, by the Member.

3.6. Place of Meetings. All meetings of the Managers may be held either within or without the State of Delaware.

3.7. Annual Meetings. The annual meeting of Managers shall be held, without further notice, immediately following the annual meeting of Member, and at the same place, or at such other time and place as shall be fixed with the consent in writing of all the Managers.

3.8. Regular Meetings. Regular meetings of the Managers may be held without notice at such time and place either within or without the State of Delaware as shall from time to time be determined by the Managers.

3.9. Special Meetings. Special meetings of the Managers may be called by any Manager on three (3) days’ notice to each Manager, either personally or by mail, telephone or by telegram.

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3.10. Quorum. At all meetings of the Managers, the presence of a Majority shall be necessary and sufficient to constitute a quorum for the transaction of business unless a greater number is required by law. At a meeting at which a quorum is present, the act of a Majority shall be the act of the Managers, except as otherwise provided by law, the Certificate or this Agreement. If a quorum shall not be present at any meeting of the Managers, the Managers present at the meeting may adjourn the meeting from time to time, without notice other than announcement at the meeting, until a quorum shall be present.

3.11. Attendance and Waiver of Notice. Attendance of a Manager at any meeting shall constitute a waiver of notice of such meeting, except where a Manager attends a meeting for the express purpose of objecting to the transaction of any business on the ground that the meeting is not lawfully called or convened. Neither the business to be transacted at, nor the purpose of, any regular or special meeting of the Managers need be specified in the notice or waiver of notice of such meeting.

3.12. Compensation. Managers, as such, shall not receive any stated salary for their services, but shall receive such compensation for their services as may be from time to time determined by the Member. In addition, a fixed sum and expenses of attendance, if any, may be allowed for attendance at each regular or special meeting of the Managers, provided that nothing contained in this Agreement shall be construed to preclude any Manager from serving the Company in any other capacity and receiving compensation for such service.

3.13. Officers. The Managers may, from time to time, designate one or more persons to be officers of the Company. No officer need be a Member or a Manager. Any officers so designated shall have such authority and perform such duties as the Managers may, from time to time, delegate to them. The Managers may assign titles to particular officers, including, without limitation, president, vice president, chief financial officer, secretary, assistant secretary, treasurer and assistant treasurer. Each officer shall hold office until such person’s successor shall be duly designated and shall qualify or until such person’s death or until such person shall resign or shall have been removed in the manner hereinafter provided. Any number of offices may be held by the same person. The salaries or other compensation, if any, of the officers and agents of the Company shall be fixed from time to time by the Managers. The Managers, whenever in their judgment the best interests of the Company will be served thereby, may remove any officer as such, either with or without cause. Any vacancy occurring in any office of the Company (other than Manager) may be filled by the Managers.

3.14. Indemnification. Each Member, Manager and officer shall be indemnified and held harmless by the Company, including advancement of expenses, but only to the extent that the Company’s assets are sufficient therefor, from and against all claims, liabilities, and expenses arising out of any act performed or omitted to be performed in connection with the management of the Company’s affairs, including reasonable attorneys’ fees incurred by such Member, Manager or officer in connection with the defense of any action based on any such act or omission, but excluding those claims, liabilities and expenses caused by the gross negligence or willful misconduct of such Member, Manager or officer, subject to all limitations and requirements imposed by the Act. These indemnification rights are in addition to any rights that any Member, Manager or officer may have against third parties. The foregoing indemnification specifically includes those claims that arise out of the indemnified party’s sole, joint or contributory

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negligence, but specifically excludes those claims that arise out of the indemnified party’s willful misconduct, fraud or gross negligence. To the extent that an indemnified party is a party to this Agreement, such indemnified party would not have entered into this Agreement if not for this indemnification.

ARTICLE IV

RIGHTS AND DUTIES OF THE MEMBER

4.1. Place of Meetings. All meetings of the Member shall be held at the principal office of the Company or at such other place within or without the State of Delaware as may be determined by the Member and set forth in any notice or waivers of notice of such meeting.

4.2. Annual and Special Meetings. The annual and special meetings of the Member for the election of Managers and the transaction of such other business as may properly come before the meeting shall be held at such time and date as shall be designated by the Member from time to time.

4.3. Actions Without a Meeting. Notwithstanding any provision contained in this Article IV, all actions of the Member provided for herein may be taken by written consent without a meeting. Any such action which may be taken by the Member without a meeting shall be effective only if the consent is in writing, sets forth the action so taken, and is signed by the Member.

4.4. Voting for Managers. Managers shall be elected by the Member.

4.5. Number. The initial number of Members of the Company shall be one (1).

4.6. Additional Members. Additional Persons may be admitted to the Company as Members and Membership Interests or Units may be created and issued to those Persons and to existing Members at the direction of the Members, on such terms and conditions as all of the Members may determine at the time of admission. The terms of admission or issuance may provide for the creation of different classes or groups of Members having different rights, powers and duties. The Managers shall reflect the creation of any new class or group in an amendment to this Agreement indicating the different rights, powers and duties, and such an amendment need be executed only by the Members. Any such admission is effective only after the new Member has executed and delivered to the Managers a document including the new Member’s notice address, and its agreement to be bound by this Agreement.

ARTICLE V

CAPITALIZATION

5.1. Capital Contributions.

(a) Upon the execution of this Agreement, the Member shall contribute cash or property to the Company in the amount set forth as the initial Capital Contribution on Exhibit B. Such cash or property shall be the Initial Capital Contribution of the Member and, upon such contribution, the Member shall receive one thousand (1,000) Units.

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(b) If at any time the Member determines that the Company has insufficient funds to carry out the purposes of the Company, the Member may make additional contributions to the capital of the Company.

(c) The Member shall not be paid interest on any Capital Contribution.

5.2. Withdrawal or Reduction of Capital Contributions.

(a) The Member shall not receive out of the Company’s property any part of its Capital Contribution until all liabilities of the Company have been paid or there remains property of the Company sufficient to pay such liabilities.

(b) The Member shall not have the right to withdraw all or any part of its Capital Contribution or to receive any return on any portion of its Capital Contribution, except as may be otherwise specifically provided in this Agreement. Under circumstances involving a return of any Capital Contribution, the Member shall not have the right to receive property other than cash.

5.3. Liability of Member. The Member shall not be liable for the debts, liabilities or obligations of the Company beyond its initial Capital Contribution. The Member shall not be required to contribute to the capital of, or to loan any funds to, the Company.

ARTICLE VI

DISTRIBUTIONS

6.1. Distributions. Subject to Section 6.2, the Company shall make all distributions at such times as determined by the Member.

6.2. Limitation Upon Distribution. No distribution shall be declared and paid unless, if after the distribution is made, the value of assets of the Company would exceed the liabilities of the Company, except liabilities to the Member on account of its Capital Contributions.

ARTICLE VII

BOOKS AND ACCOUNTS

7.1. Records and Reports. At the expense of the Company, the Managers shall maintain records and accounts of all operations and expenditures of the Company.

7.2. Returns and Other Elections. The Managers shall cause the preparation and timely filing of all tax returns required to be filed by the Company pursuant to the Code and all other tax returns deemed necessary and required in each jurisdiction in which the Company does business. All elections permitted to be made by the Company under federal or state laws shall be made by the Managers with the consent of the Member.

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ARTICLE VIII

DISSOLUTION AND TERMINATION

8.1. Dissolution.

(a) The Company shall be dissolved upon the first of the following to occur:

(b) Upon dissolution of the Company, the business and affairs of the Company shall terminate, and the assets of the Company shall be liquidated under this Article VIII.

(c) Dissolution of the Company shall be effective as of the day on which the event occurs giving rise to the dissolution, but the Company shall not terminate until there has been a winding up of the Company’s business and affairs, and the assets of the Company have been distributed as provided in Section 8.2.

(d) Upon dissolution of the Company, the Managers may cause any part or all of the assets of the Company to be sold in such manner as the Managers shall determine in an effort to obtain the best prices for such assets; provided, however, that the Managers may distribute assets of the Company in kind to the Member to the extent practicable.

8.2. Distribution of Assets Upon Dissolution. In settling accounts after dissolution, the assets of the Company shall be paid in the following order:

(a) First, to creditors, in the order of priority as provided by applicable law, except those to the Member on account of the Member’s Capital Contributions; and

(b) Second, any remainder shall be distributed to the Member.

8.3. Cancellation of Certificate. When all liabilities and obligations of the Company have been paid or discharged, or adequate provision has been made therefor, and all of the remaining property and assets of the Company have been distributed to the Member according to the Member’s rights and interests, the Certificate of Cancellation shall be executed on behalf of the Company by the Managers or the Member and shall be filed with the Secretary of State of Delaware, and the Managers and Member shall execute, acknowledge and file any and all other instruments necessary or appropriate to reflect the dissolution and termination of the Company.

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ARTICLE IX

TRANSFER OF MEMBERSHIP INTERESTS

The Member may sell, assign or otherwise transfer all or any portion of the Member’s Membership Interest at any time to any Person.

ARTICLE X

MISCELLANEOUS PROVISIONS

10.1. Notices. Any notice, demand or communication required or permitted to be given by any provision of this Agreement shall be deemed to have been sufficiently given or served for all purposes if delivered personally to the party or to an officer of the party to whom the same is directed or, if sent by registered or certified mail, postage and charges prepaid, addressed to the Member’s, Manager’s and/or Company’s address as it appears in the Company’s records, as appropriate. Except as otherwise provided herein, any such notice shall be deemed to be given when delivered personally or the next Business Day after the date on which the same was telecopied to such person.

10.2. Application of Delaware Law. This Agreement and the application or interpretation hereof, shall be governed exclusively by the laws of the State of Delaware, and specifically the Act, excluding any conflicts of laws rule or principle that might refer the governance or construction of this Agreement to the law of another jurisdiction.

10.3. Headings and Sections. The headings in this Agreement are inserted for convenience only and are in no way intended to describe, interpret, define, or limit the scope, extent or intent of this Agreement or any provision hereof. Unless the context requires otherwise, all references in this Agreement to Sections or Articles shall be deemed to mean and refer to Sections or Articles of this Agreement.

10.4. Amendments. Except as otherwise expressly set forth in this Agreement, the Certificate and this Agreement may be amended, supplemented or restated only upon the written consent of the Member. Upon obtaining the approval of any amendment to the Certificate, the Managers shall cause a certificate of amendment in accordance with the Act to be prepared, and such certificate shall be executed by no less than one Manager and shall be filed in accordance with the Act.

10.5. Number and Gender. Where the context so indicates, the masculine shall include the feminine, the neuter shall include the masculine and feminine, and the singular shall include the plural.

10.6. Binding Effect. Except as herein otherwise provided to the contrary, this Agreement shall be binding upon and inure to the benefit of the Member and the Member’s distributees, legal representatives, successors and assigns.

10.7. Counterparts. This Agreement may be executed in multiple counterparts, each of which shall be deemed to be an original and shall be binding upon the Member who executed the same, but all of such counterparts shall constitute the same Agreement.

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10.8. Severability. Except as otherwise provided in the succeeding sentence, every term and provision of this Agreement in intended to be severable, and if any term or provision of this Agreement is illegal or invalid for any reason whatsoever, such illegality or invalidity shall not affect the legality or validity of the remainder of this Agreement. The preceding sentence shall be of no force or effect if the consequence of enforcing the remainder of this Agreement without such illegal or invalid term or provision would be to cause any party to lose the benefit of its economic bargain.

IN WITNESS WHEREOF, the undersigned, being the sole Member of the Company, has caused this Agreement to be duly adopted by the Company as of the date set forth above.

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Exhibit A

Managers

Exhibit B

Initial Capital Contributions

$1,000.00