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                                                               Exhibit 10.21(b)

                            MILLENNIUM CHEMICALS INC.

                            Amendment Number 1 to the

                            MILLENNIUM CHEMICALS INC.
                            LONG TERM INCENTIVE PLAN,
                 as amended and restated as of January 26, 2001
                                  (the "Plan")

The Plan shall be, and it hereby is, amended effective June 1, 2002 as follows:

Subparagraph "(d)" of the definition of "Change in Control" in Section 2.9 of
the Plan shall be amended and restated in its entirety as follows:

     (d)  the stockholders of the Company approve a plan of complete liquidation
          of the Company or the closing of the sale or disposition by the
          Company of all or substantially all of the Company's assets other than
          the sale or disposition of all or substantially all of the assets of
          the Company to one or more Subsidiaries (as defined below) of the
          Company or to a person or persons who beneficially own, directly or
          indirectly, at least fifty percent (50%) or more of the combined
          voting power of the outstanding voting securities of the Company at
          the time of the sale or disposition provided, however, (y) the sale or
          disposition of all or any part of the Company's interests in Equistar
          Chemicals, LP ("Equistar") (and all subsequent sales and dispositions
          of any securities or assets received as proceeds thereof, or as
          proceeds of proceeds) shall not be deemed to constitute a Change in
          Control, and (z) if the Company sells or disposes of all or any part
          of the Company's interests in Equistar indirectly (either through the
          sale or other disposition of any entity that owns, directly or
          indirectly, all or any part of the Company's interests in Equistar, or
          otherwise), then the sale or disposition of the Company's interests in
          Equistar (and all subsequent sales and dispositions of any securities
          or assets received as proceeds thereof, or as proceeds of proceeds)
          shall be ignored and disregarded in determining whether any such
          Change in Control has occurred. By way of illustration, if an indirect
          subsidiary of the Company that owns the Company's interests in
          Equistar together with certain other assets is sold, then, in
          determining whether a Change in Control has occurred, all relevant
          determinations shall be made pursuant to the assumption that (y) such
          subsidiary owns only such other assets, and (z) neither such
          subsidiary nor the Company owns, either directly or indirectly, the
          interests in Equistar. Only one (1) Change in Control may take place
          under this Plan.