SUPPLEMENTAL INDENTURE

Exhibit 4.1

SUPPLEMENTAL INDENTURE

This SUPPLEMENTAL INDENTURE (this “Supplemental Indenture”), dated as of May 16, 2006, is by and among Dynegy Inc., an Illinois corporation (the “Company”), Dynegy Holdings Inc., a Delaware corporation (the “Guarantor”), and Wilmington Trust Company, as trustee (the “Trustee”), supplementing that certain Indenture, dated as of August 11, 2003, pursuant to which the Company issued its 4.75% Convertible Subordinated Debentures due 2023 (the “Debentures”). All terms used in this Supplemental Indenture that are defined in the Indenture, either directly or by reference therein, have the respective meanings assigned to them therein, except to the extent such terms are otherwise defined in this Supplemental Indenture or the context clearly requires otherwise.

RECITALS

WHEREAS, Section 9.02 of the Indenture provides that the Company and the Trustee may amend or supplement the Indenture with the consent of the Holders of at least a majority in principal amount of the Debentures;

WHEREAS, the Company has offered to convert (the “Offer”) each $1000 principal amount of the Debentures to (a)  ###-###-#### shares of Class A common stock, no par value per share, of the Company, (b) a premium of $193.85 payable in cash and (c) accrued and unpaid interest from February 15, 2006 up to, but not including, the payment date for the Conversion Offer, on the terms and subject to the conditions set forth in then Company’s Prospectus and Solicitation Statement dated April 12, 2006, as amended and supplemented, and the related Letter of Transmittal and Consent, delivered to Holders;

WHEREAS, in connection with the Offer, the Company has solicited consents (the “Consent Solicitation”) from the Holders to a proposed amendment to the Indenture to eliminate the Event of Default set forth in Section 6.01(7) of the Indenture (the “Proposed Amendment”);

WHEREAS, pursuant to the Consent Solicitation, the Holders of at least majority in principal amount of the Debentures have consented to the Proposed Amendment;

WHEREAS, the Company desires to execute and deliver, and has requested the Trustee to join with the Company and the Guarantor in the execution and delivery of, this Supplemental Indenture for the purpose of amending the Indenture to effect the Proposed Amendment;

WHEREAS, the Company has been authorized by a resolution of its Board of Directors to execute and deliver this Supplemental Indenture;

WHEREAS, this Supplemental Indenture has been duly authorized by all necessary corporate action on the part of the Guarantor; and

WHEREAS, the Company has furnished, or caused to be furnished, to the Trustee, and the Trustee has received, (i) an Officers’ Certificate complying with Sections 9.06 and 13.04 of the Indenture; and (ii) an Opinion of Counsel stating, among other things, that this Supplemental Indenture is authorized or permitted by the Indenture, as well as a certified copy of the

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resolutions of the Company’s Board of Directors authorizing the execution of this Supplemental Indenture.

NOW, THEREFORE, in consideration of the foregoing premises and for other good and valuable consideration, the receipt of which is hereby acknowledged, the Company, the Guarantor and the Trustee mutually covenant and agree for the equal and proportionate benefit of the Holders as follows:

1. Proposed Amendment. Section 6.01(7) of the Indenture hereby is deleted in its entirety and replaced with the phrase “Intentionally Omitted.” Any references to such deleted section in the Indenture hereby also are deleted in their entirety, except as otherwise provided in Section 2 below.

2. Defined Terms. The definition of the defined term “Payment Default” used in the Indenture, which definition is set forth in the section that is eliminated by this Supplemental Indenture and which defined term is still used in the Indenture after giving effect to the amendment to the Indenture set forth in this Supplemental Indenture, hereby is deemed a part of, and is deemed to be defined in, Section 1.01 (Definitions) of the Indenture, and hereby is deemed to be in alphanumeric order within Section 1.01 (Definitions) of the Indenture.

3. Effect of Supplemental Indenture. Except as modified or amended by this Supplemental Indenture, all provisions of the Indenture shall remain in full force and effect. In the event of conflict between the terms and conditions contained in the Debentures and those contained in the Indenture, as modified and amended by this Supplemental Indenture, the provisions of the Indenture, as modified and amended by this Supplemental Indenture, shall control.

4. Interpretation. Upon the execution and delivery of this Supplemental Indenture, the Indenture shall be modified and amended in accordance with this Supplemental Indenture, and all the terms and conditions of the Indenture and this Supplemental Indenture shall be read together as though they constitute one instrument, except that, in case of conflict, the provisions of this Supplemental Indenture shall control. The Indenture, as modified and amended by this Supplemental Indenture, is hereby ratified and confirmed in all respects and shall bind every Holder of the Debentures.

5. Trustee.

(a) Trustee’s Acceptance. Subject to Section 3 above, the Trustee hereby accepts this Supplemental Indenture and agrees to perform the same under the terms and conditions set forth in the Indenture.

(b) Trustee Not Responsible for Recitals. The Trustee shall not be responsible in any manner whatsoever for, or in respect of, the validity or sufficiency of this Supplemental Indenture, or for, or in respect of, the recitals contained herein, all of which recitals are made solely by the Company.

(c) Certain Duties and Responsibilities of the Trustee. In entering into this Supplemental Indenture, the Trustee shall be entitled to the benefit of every provision of the

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Indenture relating to the conduct or affecting the liability of, or affording protection to, the Trustee, whether or not elsewhere herein so provided.

6. Severability. In the event any provision of this Supplemental Indenture shall be invalid, illegal or unenforceable, the validity, legality and enforceability of the remaining provisions of this Supplemental Indenture shall not in any way be affected or impaired thereby.

7. Conflict with Trust Indenture Act. If any provision of this Supplemental Indenture limits, qualifies or conflicts with any provision of the Trust Indenture Act of 1939, as amended (the “TIA”), that is required under the TIA to be a part of or govern any provision of this Supplemental Indenture, such provision of the TIA shall control. If any provision of this Supplemental Indenture modifies or excludes any provision of the TIA that may be so modified or excluded, such provision of the TIA shall be deemed to apply to the Indenture as so modified or excluded by this Supplemental Indenture, as the case may be.

8. Benefits of this Supplemental Indenture. Nothing in this Supplemental Indenture or the Debentures, express or implied, shall give to any Person, other than the parties hereto and thereto and their successors hereunder and thereunder and the Holders of the Debentures, any benefit or any legal or equitable right, remedy or claim under the Indenture, this Supplemental Indenture or the Debentures.

9. Successors. All agreements of the Company, the Guarantor and the Trustee in this Supplemental Indenture shall bind their respective successors.

10. Governing Law. THE INTERNAL LAW OF THE STATE OF NEW YORK SHALL GOVERN AND BE USED TO CONSTRUE THIS SUPPLEMENTAL INDENTURE WITHOUT GIVING EFFECT TO APPLICABLE PRINCIPLES OF CONFLICTS OF LAW TO THE EXTENT THAT THE APPLICATION OF THE LAWS OF ANOTHER JURISDICTION WOULD BE REQUIRED THEREBY.

11. Effect of Headings. The section headings in this Supplemental Indenture have been inserted for convenience of reference only, are not to be considered a part of this Supplemental Indenture and shall in no way modify or restrict any of the terms or provisions hereof.

12. Counterparts. The parties hereto may sign multiple counterparts of this Supplemental Indenture. Each signed counterpart shall be deemed an original, but all of them together shall constitute one and the same instrument.

[Signature page follows.]

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IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed, all as of the date first written above.

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