SECOND SUPPLEMENTAL INDENTURE

SECOND SUPPLEMENTAL INDENTURE

Dated as of July 31, 2006

to

INDENTURE

Dated as of November 25, 2003

Among

MILLENNIUM CHEMICALS INC.,

MILLENNIUM AMERICA INC.

and

THE BANK OF NEW YORK

as Trustee

4% Convertible Senior Debentures

SECOND SUPPLEMENTAL INDENTURE (this “Second Supplemental Indenture”), dated as of July 31, 2006 (the “Effective Date”), among MILLENNIUM CHEMICALS INC., a corporation duly organized and existing under the laws of the State of Delaware (hereinafter called “Millennium”), 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 (together with the First Supplemental Indenture dated as of November 30, 2004 among Lyondell Chemical Company, Millennium, Guarantor and the Trustee, the “Indenture”), pursuant to which the 4% Convertible Senior Debentures of Millennium (the “Debentures”) were issued;

WHEREAS, Section 10.02 of the Indenture provides that Millennium and the Trustee, with the consent of the holders of at least a majority in aggregate principal amount of the Debentures, from time to time and at any time, may enter into an indenture supplemental to the Indenture, inter alia, to change any of the provisions of the Indenture;

WHEREAS, Millennium has requested that certain provisions of the Indenture be modified in the manner provided in this Second Supplemental Indenture, and the holders of at least a majority in aggregate principal amount of the Debentures are willing to grant their consent to such modifications;

NOW, THEREFORE, in consideration of the premises, the parties hereto hereby agree as follows:

ARTICLE ONE

DEFINITIONS

Capitalized terms used but not defined in this Second Supplemental Indenture shall have the respective meanings assigned to them in the Indenture.

ARTICLE TWO

AMENDMENTS TO INDENTURE

SECTION 2.1. Amendment to Section 1.01. Section 1.01 of the Indenture is hereby amended by inserting the following definition in the appropriate alphabetical order therein:

“Millennium Holdings, LLC” means Millennium Holdings, LLC, a Delaware limited liability company, and its successors.

SECTION 2.2. Amendments to Section 6.01.

(1) Section 6.01(i) of the Indenture is hereby amended and restated to read in its entirety as follows:

“(i) final unsatisfied judgments not covered by insurance aggregating in excess of $30,000,000 rendered against the Company or any of its subsidiaries (other than Millennium Holdings, LLC or any of its subsidiaries) and not stayed, bonded or discharged within a period of sixty (60) consecutive days; or”

(2) Section 6.01(j) of the Indenture is hereby amended and revised to read as follows:

“(j) the Company or any of its subsidiaries shall commence a voluntary case or other proceeding seeking liquidation, reorganization or other relief with respect to the Company or any of its subsidiaries (other than Millennium Holdings, LLC or any of its subsidiaries) or its debts under any bankruptcy, insolvency or other similar law now or hereafter in effect or seeking the appointment of a trustee, receiver, liquidator, custodian or other similar official of the Company or any of its subsidiaries (other than Millennium Holdings, LLC or any of its subsidiaries) or any substantial part of the property of the Company or any of its subsidiaries (other than Millennium Holdings, LLC or any of its subsidiaries), or shall consent to any such relief or to the appointment of or taking possession by any such official in an involuntary case or other proceeding commenced against the Company or the Guarantor, or shall make a general assignment for the benefit of creditors, or shall fail generally to pay its debts as they become due; or”

ARTICLE THREE

CONCERNING THE TRUSTEE

SECTION 3.1. Terms and Conditions. The Trustee accepts this Second Supplemental Indenture and agrees to perform the duties of the Trustee upon the terms and conditions set forth herein and in the Indenture.

SECTION 3.2. 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 Second Supplemental Indenture or the proper authorization or the due execution hereof by 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 Millennium or the Guarantor.

ARTICLE FOUR

EFFECT OF EXECUTION AND DELIVERY HEREOF

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

2

ARTICLE FIVE

MISCELLANEOUS PROVISIONS

SECTION 5.1. Effective Time. This Second Supplemental Indenture is effective as of the Effective Date.

SECTION 5.2. Headings Descriptive. The headings of the several Articles and Sections of this Second Supplemental Indenture are inserted for convenience only and shall not in any way affect the meaning or construction of any provision of this Second Supplemental Indenture.

SECTION 5.3. Rights and Obligations of the Trustee. 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 Second Supplemental Indenture as fully and with the same effect as if set forth herein in full.

SECTION 5.4. Successors and Assigns. This Second 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.

SECTION 5.5. Counterparts. This Second 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.

SECTION 5.6. Governing Law. This Second Supplemental Indenture shall be governed by and construed in accordance with the laws of the State of New York.

3

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

Signature Page to Second Supplemental Indenture