Exhibit 8.1

[Baker Botts L.L.P. Letterhead]

June 18, 2004

Lyondell Chemical Company

1221 McKinney, Suite 700

Houston, Texas 77010

Ladies and Gentlemen:

We are acting as counsel to Lyondell Chemical Company, a Delaware corporation (“Lyondell”), in connection with the Merger, as defined and described in the Agreement and Plan of Merger dated as of March 28, 2004 among Lyondell, Millennium Chemicals Inc., a Delaware corporation (“Millennium”), and Aries Subsidiary LLC, a Delaware limited liability company later renamed Millennium Subsidiary LLC (the “Merger Agreement”). Lyondell has filed a Registration Statement (Registration No. 333-114877) with the Securities and Exchange Commission (the “SEC”) under the Securities Act of 1933, as amended (the “Securities Act”) (the “Registration Statement”), which includes the joint proxy statement of Lyondell and Millennium and the prospectus of Lyondell (together, the “Proxy Statement/Prospectus”).

In providing this opinion, we have examined and are relying upon the truth and accuracy at all relevant times of the statements, covenants, and representations contained in (i) the Merger Agreement, (ii) the Proxy Statement/Prospectus, (iii) certain other filings made by Lyondell and Millennium with the SEC and (iv) other information provided to us by Lyondell. In addition, we assume that the Merger will be consummated in accordance with the Merger Agreement and as described in the Proxy Statement/Prospectus.

Subject to the assumptions set forth above and the assumptions and qualifications set forth in the discussion in the Proxy Statement/Prospectus under the headings “Proposals to Approve the Proposed Transaction—Material U.S. Federal Income Tax Consequences of the Proposed Transaction—Opinions of Counsel” and “—Scope of Discussion” (the “Discussion”), we hereby confirm the opinion of Baker Botts L.L.P. which is attributed to us in the Discussion. Except as specifically described herein, we express no opinion as to the United States federal, state, local, foreign, or other tax consequences of the Merger. As indicated in the Discussion, no ruling will be requested from the Internal Revenue Service (the “IRS”) on any aspect of the Merger. Our opinion is not binding upon the IRS or a court and will not preclude the IRS or a court from adopting a contrary position.

Lyondell Chemical Company 2 June 18, 2004

This letter is furnished to you solely for use in connection with the Merger and is not to be relied upon by any other person, quoted in whole or in part, or otherwise referred to (except in a list of closing documents) without our express written consent. We hereby consent to the filing of this letter as an exhibit to the Registration Statement and to the reference to our firm name under the headings “Questions and Answers About the Proposed Transaction,” “Proposals to Approve the Proposed Transaction —Material U.S. Federal Income Tax Consequences of the Proposed Transaction—Opinions of Counsel” and “Legal Matters” in the Proxy Statement/Prospectus. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the SEC thereunder.

Sincerely,

/s/ Baker Botts L.L.P.