Exhibit 5.1

[Baker Botts L.L.P. Letterhead]

016119.0312

June 18, 2004

Lyondell Chemical Company

1221 McKinney St.

Houston, Texas 77010

Ladies and Gentlemen:

As set forth in the Registration Statement on Form S-4, as amended, 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 proposed issuance of up to 81,887,907 shares (the “Shares”) of Lyondell’s common stock, par value $1.00 per share (“Lyondell Common Stock”), we are passing upon certain legal matters in connection with the Shares for Lyondell. The Shares are to be issued in connection with the merger (the “Merger”) of Millennium Subsidiary LLC, a Delaware limited liability company (“Merger Sub”), with and into Millennium Chemicals Inc., a Delaware corporation (“Millennium”), pursuant to the terms of the Agreement and Plan of Merger, dated March 28, 2004 (the “Agreement”), among Lyondell, Millennium and Merger Sub. In the Merger, shares of Millennium’s common stock will be converted into the right to receive Shares. 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, and the Certificate of Incorporation of Lyondell to be effective as of the effective time of the Merger, 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.

In rendering this opinion, we assume that, immediately prior to the effective time of the Merger, Millennium will be a corporation duly organized and validly existing in good standing under the laws of the State of Delaware, and that all the shares of Millennium’s common stock outstanding immediately prior to the effective time of the Merger will be duly authorized, validly issued, fully paid and nonassessable.

Lyondell Chemical Company 2 June 18, 2004

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

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

2. When the required approval of the shareholders of Lyondell has been obtained as set forth in the Agreement, upon the issuance by Lyondell of the Shares upon consummation of the Merger pursuant to the Agreement, such Shares will be duly authorized, validly issued, fully paid and nonassessable.

This opinion is limited in all respects to the General Corporation Law of the State of Delaware.

We hereby consent to the reference to our Firm under the caption “Legal Matters” in the Joint Proxy Statement/Prospectus included in the Registration Statement on Form S-4 and to the filing of this opinion with the Commission as Exhibit 5.1 to the Registration Statement on Form S-4. 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.