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                                                                    Exhibit 31.1


                      CERTIFICATION PURSUANT TO SECTION 302
                        OF THE SARBANES-OXLEY ACT OF 2002

I, Robert E. Lee, President and Chief Executive Officer of Millennium Chemicals
Inc., certify that:

1. I have reviewed this annual report on Form 10-K of Millennium Chemicals Inc.
as filed with the Securities and Exchange Commission on March 12, 2004 and as
amended by Amendment No. 1 to the Annual Report on Form 10-K, filed with the
Securities and Exchange Commission on April 27, 2004, Amendment No. 2 to the
Annual Report on Form 10-K, filed with the Securities and Exchange Commission on
August 9, 2004, Amendment No. 3 to the Annual Report on Form 10-K, filed with
the Securities and Exchange Commission on September 23, 2004 and this Amendment
No. 4 to the Annual Report on Form 10-K, filed with the Securities and Exchange
Commission on the date hereof; and

2. Based on my knowledge, this annual report, as amended, does not contain any
untrue statement of a material fact or omit to state a material fact necessary
to make the statements made, in light of the circumstances under which such
statements were made, not misleading with respect to the period covered by this
annual report;

3. [Intentionally Omitted];

4. The registrant's other certifying officer and I are responsible for
establishing and maintaining disclosure controls and procedures (as defined in
Exchange Act Rules 13a-15(e) and 15d-15(e)) for the registrant and have:

         a) designed such disclosure controls and procedures, or caused such
         disclosure controls and procedures to be designed under our
         supervision, to ensure that material information relating to the
         registrant, including its consolidated subsidiaries, is made known to
         us by others within those entities, particularly during the period in
         which this annual report is being prepared;

         b) evaluated the effectiveness of the registrant's disclosure controls
         and procedures and presented in this report our conclusions about the
         effectiveness of the disclosure controls and procedures, as of the end
         of the year covered by this report based on such evaluation; and

         c) disclosed in this report any change in the registrant's internal
         control over financial reporting that occurred during the registrant's
         most recent fiscal quarter (the registrant's fourth fiscal quarter in
         the case of an annual report) that




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         has materially affected, or is reasonably likely to materially affect,
         the registrant's internal control over financial reporting; and

5. The registrant's other certifying officer and I have disclosed, based on our
most recent evaluation of internal control over financial reporting, to the
registrant's auditors and the audit committee of the registrant's board of
directors (or persons performing the equivalent functions):

         a) all significant deficiencies and material weaknesses in the design
         or operation of internal controls over financial reporting which are
         reasonably likely to adversely affect the registrant's ability to
         record, process, summarize and report financial information; and

         b) any fraud, whether or not material, that involves management or
         other employees who have a significant role in the registrant's
         internal controls over financial reporting.

Date: September 24, 2004

                                           /s/ ROBERT E. LEE
                                           -----------------------------------
                                           Robert E. Lee
                                           President and Chief Executive Officer
                                           (Principal Executive Officer)