PLAINS EXPLORATION & PRODUCTION COMPANY FIRST AMENDMENT TO EMPLOYMENT AGREEMENT

Exhibit 10.26

PLAINS EXPLORATION & PRODUCTION COMPANY

FIRST AMENDMENT TO

EMPLOYMENT AGREEMENT

WHEREAS, effective as of June 9, 2004, Plains Exploration & Production Company (the “Company”) entered into an employment agreement (the “Agreement”) with Stephen A. Thorington (the “Employee”); and

WHEREAS, the Company and the Employee have agreed to amend the Agreement as set forth below;

NOW, THEREFORE, the Company and the Employee agree as follows:

1. Paragraph 4(b) of the Agreement shall be amended by adding the following sentence thereto:

“Such bonus, if any, shall be paid not later than the fifteenth day of the third calendar month following the later of (i) the last day of the calendar year or (ii) the last day of the Company’s fiscal year in which the calendar year ends.”

2. Paragraph 6(c)(ix) shall be added to the Agreement to read as follows:

“Notwithstanding the foregoing or anything herein to the contrary, if any amounts payable hereunder are reasonably determined by the Company to be “nonqualified deferred compensation” payable to a “specified employee” upon “separation from service” (within the meaning of section 409A of the Internal Revenue Code of 1986 as amended and any applicable regulations or other guidance issued pursuant thereto (the “Code”)) then such amounts shall not be paid upon separation from service, but shall be paid as described below. As soon as administratively feasible upon the Employee’s separation from service, or, if earlier, upon a Change of Control, the maximum amount which may become payable to Employee after separation from service shall be contributed to the trustee of a “rabbi” trust substantially in the form attached hereto (the “Trust”). Such amounts that would otherwise be payable upon separation from service shall be held by the trustee pursuant to the terms of such Trust and paid to Employee as soon as administratively feasible following the earlier of: (1) the first day that is six months following his separation from service; or (2) Employee’s date of death. Such amounts that would otherwise be payable in installments commencing on separation from service shall be accumulated and paid in a lump sum on the date that is the earlier of (1) or (2) above and shall be paid in installments thereafter.”

3. Paragraph 6(h) of the Agreement shall be amended to read as follows:

“(h) Full Tax Gross-Up of Excise Payments. In the event that any payment, award, benefit or distribution (or any acceleration of any payment, award, benefit or distribution) made or provided to or for the benefit of Employee in connection with this Agreement, or Employee’s employment with Company or the termination thereof (the “Payments”) is determined to be subject to the excise tax imposed by Section 4999 or 409A of the Code or any interest or penalties with respect to such excise taxes (such excise taxes, together with any such interest and penalties, are collectively referred to as the “Excise Taxes”), then the Employee shall be entitled to receive an additional payment (a “Gross-Up Payment”) from Company such that the net amount received by the Employee after paying any applicable Excise Taxes and any federal, state or local income or FICA taxes on such Gross-Up Payment, shall be equal to the amount Employee would have received if such Excise Taxes were not applicable to the Payments.

For purposes of determining whether any of the Payments will be subject to the Excise Taxes and the amount of such Excise Taxes, (i) all of the Payments shall be treated as “parachute payments” (within the meaning of Section 280G(b)(2) of the Code) unless, in the opinion of tax counsel (“Tax Counsel”) reasonably acceptable to the Employee, such payments or benefits (in whole or in part) do not constitute parachute payments, including by reason of Section 280G(b)(4)(A) of the Code; (ii) all “excess parachute payments” within the meaning of Section 280G(b)(1) of the Code shall be treated as subject to the Excise Tax unless, in the opinion of Tax Counsel, such excess parachute payments (in whole or in part) represent reasonable compensation for services actually rendered (within the meaning of Section 280G(b)(4)(B) of the Code) in excess of the base amount (as the term “base amount” is defined in Section 280G(b)(3) of the Code) allocable to such reasonable compensation, or are otherwise not subject to the Excise Tax; (iii) the value of any noncash benefits or any deferred payment or benefit shall be determined by the Tax Counsel in accordance with the principles of Sections 280G(d) and 409A of the Code; and (iv) all Payments shall be deemed subject to the Excise Tax pursuant to section 409A of the Code unless, in the opinion of Tax Counsel, such Payments are not subject to Excise Tax pursuant to section 409A. For purposes of determining the amount of the Additional Payment, the Employee shall be deemed to pay federal income tax at the highest marginal rate of federal income taxation in the calendar year in which the Total Payments are made and State and local income taxes at the highest marginal rate of taxation in the State and locality of the Employee’s residence on the date the Total Payments are made, net of the maximum reduction in federal income taxes which could be obtained from deduction of such State and local taxes.

In the event that the Excise Taxes are determined by the IRS, on audit or otherwise, to exceed the amount taken into account hereunder in calculating the Gross-Up Payment (including by reason of any payment the existence or amount of which cannot be determined at the time of the Gross-Up Payment), the

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Company shall make another Gross-Up Payment in respect of such excess (plus any interest, penalties or additions payable by the Employee with respect to such excess) within the ten (10) business days immediately following the date that the amount of such excess is finally determined. The Employee and the Company shall each reasonably cooperate with the other in connection with any administrative or judicial proceedings concerning the existence or amount of liability for Excise Tax with respect to the Total Payments.

If a termination of the Employee’s employment shall have occurred, the Company shall promptly reimburse to the Employee all reasonable attorneys fees and expenses necessarily incurred by the Employee in disputing in good faith any issue with the Company or its affiliates pursuant to this Agreement or asserting in good faith any claim, demand or cause of action against the Company or its affiliates pursuant to this Agreement. Such payments shall be made within ten (10) business days after delivery of the Employee’s written requests for payment accompanied with such evidence of fees and expenses incurred as the Company reasonably may require.

The Gross-Up Payments provided to the Employee shall be made not later than the tenth (10^th) business day following the last date the Payments are made; provided, however, that if the amounts of such payments cannot be finally determined on or before the due date of any Excise Tax return required as a result of the Payments, the Company shall pay to the Employee on or before thirty (30) days preceding the due date of the Excise Tax return, an estimate of the Payments due, as determined in good faith by the Employee and the Company, the estimate to be of the minimum amount of such payments to which the Employee is clearly entitled, and shall pay the remainder of such payments together with interest on the unpaid remainder (or on all such payments to the extent the Company fails to make such payments when due) at 120% of the rate provided in Section 1274(b)(2)(B) of the Code as soon as the amount thereof can be determined but in no event later than sixty (60) days after the date the Total Payments are made. In the event that the amount of the estimated payment exceeds the amount subsequently determined to have been due, such excess shall constitute a non-interest bearing loan by the Company to the Employee, payable on the tenth (10^th) business day after demand by the Company. At the time the payments are made under this Agreement, the Company shall provide the Employee with a written statement setting forth the manner in which such payments were calculated and the basis for such calculations, including, without limitations any opinions or other advice the Company has received from Tax Counsel or other advisors or consultants and any such opinions or advice which are in writing shall be attached to the statement.”

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IN WITNESS WHEREOF, the Company and the Employee have executed this First Amendment on the 10th day of February, 2006 effective for all purposes as provided above.

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