FIRST AMENDMENT TO THE DYNEGY INC. SEVERANCE PAY PLAN

Exhibit 10.1

FIRST AMENDMENT TO THE

DYNEGY INC. SEVERANCE PAY PLAN

WHEREAS, Dynegy Inc. (the “Company”) and certain subsidiaries and affiliated entities have heretofore established and maintain the Dynegy Inc. Severance Pay Plan (the “Plan”);

WHEREAS, the Company has heretofore amended and restated the Plan effective February 1, 2005 on behalf of itself and all of its subsidiaries and affiliated entities that participate in the Plan;

WHEREAS, the Company established the First Supplemental Plan to the Plan, as amended (the “First Supplemental Plan”) effective June 22, 2005 on behalf of itself and all of its subsidiaries and affiliated entities that participate in the Plan;

WHEREAS, Article VII of the Plan provides that the Company may amend the Plan at any time;

WHEREAS, Article V of the First Supplemental Plan provides that the Company may amend the First Supplemental Plan at any time prior to a “Change in Control” (as defined in the First Supplemental Plan);

WHEREAS, the Company, Dynegy Holdings Inc., Dynegy Midstream Holdings, Inc., Dynegy Midstream G.P., Inc. and Targa Resources, Inc., Targa Resources Partners OLP LP and Targa Midstream GP, LLC (collectively, “Targa”) have entered into that certain Partnership Interest Purchase Agreement (“PIPA”) dated as of August 2, 2005 pursuant to which Targa will acquire all of the outstanding partnership interests of Dynegy Midstream Services, Limited Partnership (“DMS, LP”); and

WHEREAS, Section 7.1(c) of the PIPA provides that, effective immediately prior to the closing of the transactions contemplated by the PIPA (the “Closing”), all Business Employees (as such term is defined in the PIPA) shall cease to participate in the Sellers’ Benefit Plans (as such term is defined in the PIPA), and the Company desires to accomplish such cessation with respect to the Plan (and the First Supplemental Plan thereto) by an amendment terminating the participation of DMS, LP therein;

NOW THEREFORE, the Plan (including the First Supplemental Plan thereto) is hereby amended as follows, contingent upon, and effective immediately prior to, the Closing:

1. The participation of DMS, LP as an “Employer” or “Employing Company” under the Plan (and the First Supplemental Plan thereto) is hereby terminated. Attachment A to the Plan is hereby deleted and the revised Attachment A attached hereto is substituted therefor.

2. No individual who is a Business Employee is entitled to receive benefits under the Plan (or the First Supplemental Plan thereto).

3. Neither Targa nor any of its affiliates shall be deemed an “Employer” or “Employing Company” for purposes of the First Supplemental Plan.

4. Except as modified herein, the Plan (and the First Supplemental Plan thereto) shall remain in full force and effect

EXECUTED this 31st day of October, 2005.

-2-

Attachment A

Subsidiaries and Affiliates

Participating in the

Dynegy Inc. Severance Pay Plan

-3-