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IRS # 522183153
CIK # 0001091862


                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C.  20549


                                  SCHEDULE 13G



                  Under the Securities Exchange Act of 1934*


                             CROMPTON CORPORATION
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                                (Name of Issuer)

                                 Common Stock
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                         (Title of Class of Securities)

                                   227116100
                        ------------------------------
                                 (CUSIP Number)

                               December 31, 2002
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            (Date of Event Which Requires Filing of this Statement)


Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:

     [x] Rule 13d-1(b)

     [_] Rule 13d-1(c)

     [_] Rule 13d-1(d)


*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter the
disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).

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  CUSIP NO.  227116100
           -------------

      Barrow, Hanley, Mewhinney & Strauss, Inc.
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      NAMES OF REPORTING PERSONS.
 1    I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY).

          752403190
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      CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)
 2                                                              (a) [_]
                                                                (b) [_]
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      SEC USE ONLY
 3

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      CITIZENSHIP OR PLACE OF ORGANIZATION
 4
         a Nevada Corporation
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                          SOLE VOTING POWER
                     5
     NUMBER OF
                          1,139,719
      SHARES       -----------------------------------------------------------
                          SHARED VOTING POWER
   BENEFICIALLY      6

     OWNED BY             7,291,705
                   -----------------------------------------------------------
       EACH               SOLE DISPOSITIVE POWER
                     7
    REPORTING
                          8,431,424
      PERSON       -----------------------------------------------------------
                          SHARED DISPOSITIVE POWER
       WITH          8

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      AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
 9
      8,431,424
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      CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES
10    (SEE INSTRUCTIONS)
                                                                    [_]
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      PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)
11
      7.41%
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      TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)
12
      1A
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Item 1

     (a) Name of Issuer    Crompton Corporation

     (b) Address of Issuer's Principal Executive Offices

         199 Benson Road
         Middlebury, CT. 06749

Item 2

     (a) Name of Person Filing    Barrow, Hanley, Mewhinney & Strauss, Inc.

     (b) Address of Principal Business Office or, if none, Residence

         One McKinney Plaza
         3232 McKinney Avenue
         15th Floor
         Dallas, TX 75204-2429

     (c) Citizenship      a Nevada Corporation

     (d) Title of Class of Securities    Common Stock

     (e) CUSIP Number    227116100

Item 3. If this statement is filed pursuant to Rules 13d-1(b), or
        13d-2(b):
              The reporting person is an Investment Adviser registered under
              Section 203 of the Investment Advisers Act of 1940.

Item 4. Ownership.

     Provide the following information regarding the aggregate number and
percentage of the class of securities of the issuer identified in Item 1.

     (a)  Amount beneficially owned:     8,431,424

     (b)  Percent of class:  7.41%


     (c)  Number of shares as to which the person has:

          (i)   Sole power to vote or to direct the vote
                  1,139,719

          (ii)  Shared power to vote or to direct the vote
                  7,291,705

          (iii) Sole power to dispose or to direct the disposition of
                  8,431,424

          (iv)  Shared power to dispose or to direct the disposition of :
                  ---

     Instruction. For computations regarding securities which represent a right
to acquire an underlying security see (S)240.13d-3(d)(1).

Item 5.  Ownership of Five Percent or Less of a Class.

              Not Applicable

Instruction: Dissolution of a group requires a response to this item.


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Item 6.  Ownership of More than Five Percent on Behalf of Another Person.

     If any other person is known to have the right to receive or the power to
direct the receipt of dividends from, or the proceeds from the sale of, such
securities, a statement to that effect should be included in response to this
item, and if such interest relates to more than five percent of the class, such
person should be identified. A listing of the shareholders of an investment
company registered under the Investment Company Act of 1940 or the beneficiaries
of the employee benefit plan, pension fund or endowment fund is not required.

Item 7.  Identification and Classification of the Subsidiary Which Acquired the
         Security Being Reported on by the Parent Holding Company.

     If a parent holding company has filed this schedule, pursuant to Rule
13d-1(b)(ii)(G), so indicate under Item 3(g) and attach an exhibit stating
the identity and the Item 3 classification of the relevant subsidiary. If a
parent holding company has filed this schedule pursuant to Rule 13d-1(c) or Rule
13d-1(d), attach an exhibit stating the identification of the relevant
subsidiary.

Item 8.  Identification and Classification of Members of the Group.

     If a group has filed this schedule pursuant to (S)240.13d-1(b)(1)(ii)(J),
so indicate under Item 3(j) and attach an exhibit stating the identity and Item
3 classification of each member of the group. If a group has filed this schedule
pursuant to (S)240.13d-1(c) or (S)240.13d-1(d), attach an exhibit stating the
identity of each member of the group.

Item 9.  Notice of Dissolution of a Group

     Notice of dissolution of a group may be furnished as an exhibit stating
the date of the dissolution and that all further filings with respect to
transactions in the security reported on will be filed, if required, by members
of the group, in their individual capacity. See Item 5.

Item 10. Certification

         By signing below the undersigned certifies that, to the best of its
         knowledge and belief, the securities referred to above were acquired in
         the ordinary course of business and were not acquired for the purpose
         of and do not have the effect of changing or influencing the control of
         the issuer of such securities and were not acquired in connection with
         or as a participant in any transaction having such purpose or effect.


                                   SIGNATURE

     After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.


                                       Barrow, Hanley, Mewhinney & Strauss, Inc.

                                       By:  /s/ James P. Barrow
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                                                          Signature

                                                James P. Barrow / President
                                           ----------------------------------
                                                          Name/Title

February 8, 2003

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