Exhibit 5.1

[Letterhead of Baker Botts L.L.P.]

April 8, 2005

Lyondell Chemical Company

1221 McKinney St.

Houston, Texas 77010

Ladies and Gentlemen:

As set forth in the Registration Statement on Form S-3, as amended (the “Registration Statement”), to be filed by Lyondell Chemical Company, a Delaware corporation (“Lyondell”), with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), relating to the issuance from time to time pursuant to Rule 415 under the Act of shares of Lyondell’s common stock, par value $1.00 per share (the “Shares”), upon conversion of the 4% convertible senior debentures due November 15, 2023 (the “Debentures”) of Millennium Chemicals Inc., a Delaware corporation (“Millennium”), we are passing upon certain legal matters for Lyondell in connection with the Shares. The Debentures are governed by an Indenture dated November 25, 2003 among Millennium, Millennium America Inc., a Delaware corporation and an indirect, wholly-owned subsidiary of Millennium, as guarantor, and The Bank of New York, as trustee (as amended and supplemented on or before the date hereof, the “Indenture”). At your request, we are furnishing this opinion to you for filing as Exhibit 5.1 to the Registration Statement.

In our capacity as your counsel in the connection referred to above, we have examined the Certificate of Incorporation and By-laws of Lyondell, each as amended to date, and the originals, or copies certified or otherwise identified, of corporate records of Lyondell, including minute books of Lyondell as furnished to us by Lyondell, the Agreement and Plan of Merger, dated March 28, 2004, among Lyondell, Millennium and Millennium Subsidiary LLC, a Delaware limited liability company and wholly owned subsidiary of Millennium (the “Merger Agreement”), the Indenture, certificates of public officials and of representatives of Lyondell, statutes and other instruments and documents as a basis for the opinions hereinafter expressed. In giving such opinions, we have relied upon certificates of officers of Lyondell and of public officials with respect to the accuracy of the material factual matters contained in such certificates.

Based on our examination and assumptions as aforesaid, we are of the opinion that:

1. Lyondell is a corporation duly organized and validly existing under the laws of the State of Delaware.

2. The Shares have been duly authorized and, when the Shares have been duly issued upon conversion of the Debentures in accordance with the terms thereof and the Indenture, then the Shares will be validly issued, fully paid and nonassessable.

This opinion is limited in all respects to (1) the laws of the State of New York, (2) the General Corporation Law of the State of Delaware, which includes the statutory provisions and also all applicable provisions of the Delaware Constitution and reported judicial decisions interpreting these laws, and (3) applicable federal laws.

We hereby consent to the reference to our Firm under the caption “Legal Opinion” in the Prospectus included in the Registration Statement on Form S-3 and to the filing of this opinion with the Commission as Exhibit 5.1 to the Registration Statement on Form S-3. In giving such consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ Baker Botts L.L.P.