LYONDELL CHEMICAL COMPANY, MILLENNIUM CHEMICALS INC.

Exhibit 4.3(a)

EXECUTION VERSION

LYONDELL CHEMICAL COMPANY,

MILLENNIUM CHEMICALS INC.

AND

MILLENNIUM AMERICA INC.

TO

THE BANK OF NEW YORK

as Trustee

FIRST SUPPLEMENTAL INDENTURE

Dated as of November 30, 2004

to

INDENTURE

Dated as of November 25, 2003

4% Convertible Senior Debentures

FIRST SUPPLEMENTAL INDENTURE, dated as of November 30, 2004 (the “First Supplemental Indenture”), among LYONDELL CHEMICAL COMPANY, a corporation duly organized and existing under the laws of the State of Delaware (hereinafter called “Lyondell”), having its principal office at 1221 McKinney Street, Suite 700, Houston, Texas 77010, MILLENNIUM CHEMICALS INC., a corporation duly organized and existing under the laws of the State of Delaware (hereinafter called “Millennium”), having its principal office at 20 Wight Avenue, Suite 100, Hunt Valley, Maryland 21030, MILLENNIUM AMERICA INC., a corporation duly organized and existing under the laws of the State of Delaware and a wholly owned subsidiary of Millennium (hereinafter called the “Guarantor”), and THE BANK OF NEW YORK, a New York banking corporation, as Trustee (hereinafter called the “Trustee”).

RECITALS

WHEREAS, Millennium and the Guarantor have executed and delivered to the Trustee that certain Indenture, dated as of November 25, 2003 (the “Indenture”), pursuant to which the 4% Convertible Senior Debentures of Millennium (the “Debentures”) were issued;

WHEREAS, pursuant to the terms of the Indenture, the Debentures were convertible into shares of common stock, par value $0.01 per share, of Millennium (“Millennium Common Stock”) prior to the effective time of this First Supplemental Indenture;

WHEREAS, pursuant to an Agreement and Plan of Merger dated March 28, 2004 (the “Merger Agreement”), among Lyondell, Millennium and Millennium Subsidiary LLC, a limited liability company duly formed and existing under the laws of the State of Delaware formerly known as Aries Subsidiary LLC (“Millennium Merger Sub”), Millennium Merger Sub will be merged with and into Millennium (the “Merger”), with Millennium to be the surviving corporation, as a result of which each issued and outstanding share of Millennium Common Stock (other than shares of Millennium Common Stock held by Lyondell, Millennium or their respective subsidiaries) will be convertible into shares of common stock, par value $1.00 per share, of Lyondell (“Lyondell Common Stock”);

WHEREAS, in connection with the Merger, Lyondell, Millennium and the Guarantor have duly determined to make, execute and deliver to the Trustee this First Supplemental Indenture in order to reflect the results of the Merger as required by the Indenture;

WHEREAS, Section 11.01 of the Indenture requires that certain conditions be met prior to any merger of Millennium with any other Person;

WHEREAS, Section 15.06 of the Indenture requires that, as a result of the Merger, the Debentures become convertible into the consideration to be issued in the Merger to the holders of Millennium Common Stock;

WHEREAS, Section 10.01 of the Indenture provides that under certain conditions Millennium, the Guarantor and the Trustee, without the consent of the holders of Debentures, from time to time and at any time, may enter into an indenture supplemental to the Indenture, inter alia, to make provision with respect to the conversion rights of the holders of Debentures pursuant to the requirements of Section 15.06 of the Indenture.

NOW, THEREFORE, THIS FIRST SUPPLEMENTAL INDENTURE WITNESSETH:

For and in consideration of the premises, it is mutually agreed, for the equal and proportionate benefit of the respective holders from time to time of the Debentures, as follows:

ARTICLE ONE

DEFINITIONS

Except as set forth in Section 1.2, capitalized terms used but not defined in this First Supplemental Indenture shall have the respective meanings assigned to them in the Indenture.

From and after the effective time of this First Supplemental Indenture, the definitions of the following terms set forth in Article I of the Indenture shall be amended and restated to read in full as follows:

“Board of Directors” means the Board of Directors of the Company or a committee of such Board duly authorized to act for it hereunder or, if such term is used in reference to Lyondell, the Board of Directors of Lyondell or a committee of such Board duly authorized to act for it hereunder.

“Common Stock” means any stock of any class of Lyondell which has no preference in respect of dividends or of amounts payable in the event of any voluntary or involuntary liquidation, dissolution or winding up of Lyondell and which is not subject to redemption by Lyondell. Subject to the provisions of Section 15.06, however, shares issuable on conversion of Debentures shall include only shares of the class designated as Common Stock of Lyondell at November 30, 2004 (namely, the Common Stock, par value $1.00 per share) or shares of any class or classes resulting from any reclassification or reclassifications thereof and which have no preference in respect of dividends or of amounts payable in the event of any voluntary or involuntary liquidation, dissolution or winding up of Lyondell and which are not subject to redemption by Lyondell; provided that if at any time there shall be more than one such resulting class, the shares of each such class then so issuable on conversion shall be substantially in the proportion which the total number of shares of such class resulting from all such reclassifications bears to the total number of shares of all such classes resulting from all such reclassifications. The term “Common Stock” shall not mean shares of Series B Common Stock, par value $1.00 per share, of Lyondell.

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ARTICLE TWO

MERGER

SECTION 2.1. Merger.

(1) Millennium hereby represents that immediately after giving effect to the Merger, no Event of Default, and no event which, after notice or lapse of time or both, would become an Event of Default, shall have occurred and be continuing.

(2) Concurrently with the execution and delivery of this First Supplemental Indenture, Millennium has delivered to the Trustee an Officers’ Certificate and an Opinion of Counsel as required by Sections 10.05 and 11.03 of the Indenture.

ARTICLE THREE

CONCERNING THE DEBENTURES

SECTION 3.1. Conversion Privilege.

Each Debenture outstanding on the date hereof shall, from and after the effective time of this First Supplemental Indenture, during the period such Debenture shall be convertible as specified in Section 15.01 of the Indenture, be convertible into the number of shares of Lyondell Common Stock, and cash in lieu of fractional shares of Lyondell Common Stock, receivable upon the effectiveness of the Merger by a holder of the number of shares of Millennium Common Stock into which such Debenture might have been converted immediately prior to the Merger, subject to adjustment as provided in Section 15.05 of the Indenture, as such Section is amended by this First Supplemental Indenture.

SECTION 3.2. Conversion Rate and Price.

Upon the effective time of the Merger, the Conversion Rate shall be 69.6890 shares¹ of Lyondell Common Stock, and the Conversion Price shall be $14.3495.² Subsequent to the effective time of this First Supplemental Indenture, the Conversion Rate and the Conversion Price shall be adjusted from time to time as provided for in Article 15 of the Indenture, as such Article is amended by this First Supplemental Indenture.

From and after the effective time of this First Supplemental Indenture, all references to “the Company” in Sections 15.01(b), 15.02(b), 15.02(c), 15.02(g)(i), 15.02(g)(ii), 15.02(h), 15.05, 15.06, 15.07, 15.08, 15.09 and 15.10 of the Indenture shall be deemed to refer to Lyondell, unless the context shall otherwise require. Notwithstanding the foregoing, any requirement to provide notices, make announcements or file documents with the Trustee in Article 15 of the Indenture shall remain the responsibility of Millennium, and Lyondell shall not

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be responsible for such notices, announcements or filings. The term “Original Issuance Date” as used in Section 15.05(i)(iii) shall be deemed to refer to the effective time of this First Supplemental Indenture.

ARTICLE FOUR

CONCERNING THE TRUSTEE

SECTION 4.1. Terms and Conditions.

The Trustee accepts this First Supplemental Indenture and agrees to perform the duties of the Trustee upon the terms and conditions herein and in the Indenture set forth.

SECTION 4.2. No Responsibility.

The Trustee makes no undertaking or representations in respect of, and shall not be responsible in any manner whatsoever for and in respect of, the validity or sufficiency of this First Supplemental Indenture or the proper authorization or the due execution hereof by Lyondell, Millennium or the Guarantor or for or in respect of the recitals and statements contained herein, all of which recitals and statements are made solely by Lyondell, Millennium or the Guarantor.

ARTICLE FIVE

EFFECT OF EXECUTION AND DELIVERY HEREOF

From and after the effective time of this First Supplemental Indenture, (i) the Indenture shall be deemed to be amended and modified as provided herein, (ii) this First Supplemental Indenture shall form a part of the Indenture, (iii) except as modified and amended by this First Supplemental Indenture, the Indenture shall continue in full force and effect, (iv) the Debentures shall continue to be governed by the Indenture, as modified and amended by this First Supplemental Indenture, and (v) every holder of Debentures heretofore and hereafter authenticated and delivered under the Indenture shall be bound by this First Supplemental Indenture.

ARTICLE SIX

OBLIGATIONS UNDER THE INDENTURE

Notwithstanding anything in the Indenture or this First Supplemental Indenture to the contrary, all obligations for payment of principal of, or interest or premium on, the Debentures and for payment of the Guaranteed Obligations shall remain solely the obligations of Millennium and the Guarantor, respectively. Lyondell has executed this First Supplemental Indenture only for the purpose of confirming its obligation to issue its common stock upon the conversion of Debentures as set forth herein, and Lyondell neither has nor assumes any

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obligations for payment of principal of, or interest or premium on, the Debentures, any obligations as guarantor thereof or any other obligations under the Indenture.

ARTICLE SEVEN

MISCELLANEOUS PROVISIONS

This First Supplemental Indenture is effective as of the Effective Time of the Merger, as defined in the Merger Agreement.

The headings of the several Articles and Sections of this First Supplemental Indenture are inserted for convenience only and shall not in any way affect the meaning or construction of any provision of this First Supplemental Indenture.

All of the provisions of the Indenture with respect to the rights, privileges, immunities, powers and duties of the Trustee shall be applicable in respect of this First Supplemental Indenture as fully and with the same effect as if set forth herein in full.

This First Supplemental Indenture shall be binding upon and inure to the benefit of and be enforceable by the respective successors and assigns of the parties hereto and the holders of any Debentures then outstanding.

This First Supplemental Indenture may be executed in several counterparts, each of which shall be an original and all of which shall constitute but one and the same instrument.

This First Supplemental Indenture shall be governed by and construed in accordance with the laws of the State of New York.

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IN WITNESS WHEREOF, the parties hereto have caused this First Supplemental Indenture to be duly as of the day and year first above written.

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