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

                                    FORM 13F

                               FORM 13F Cover Page



            Report for the Calendar Year or Quarter Ended: September 30, 2011

Check here if Amendment:           |_|; Amendment Number: ____

This Amendment (Check only one):   |_| is a restatement
                                   |_| adds new holding entries.

Institutional Manager Filing this Report:

Name:     Two Sigma U.S. Small Cap Core Equity Fund, LP

Address:  379 West Broadway
          5th Floor
          New York, New York 10012

13F File Number: 028-14382


The institutional investment manager filing this report and the person by whom
it is signed hereby represent that the person signing the report is authorized
to submit it, that all information contained  herein is true, correct and
complete, and that it is understood that all required items, statements,
schedules, lists, and tables are considered integral parts of this form.


Person Signing this Report on Behalf of Reporting Manager:

Name:   Matthew B. Siano, Esq.
Title:  Authorized Person
Phone:  (212) 625-5712


Signature, Place and Date of Signing:

 /s/ Matthew B. Siano            New York, New York          November 14, 2011
-----------------------     --------------------------    ----------------------
     [Signature]                   [City, State]                  [Date]



Report Type:  (Check only one):

[_]      13F HOLDINGS REPORT.  (Check here if all holdings of this reporting
         manager are reported in this report).

[X]      13F NOTICE.  (Check here if no holdings reported are in this report,
         and all holdings are reported by other reporting managers(s).)

[_]      13F COMBINATION REPORT.  (Check here if a portion of the holdings for
         this reporting manager are reported in this report and a portion are
         reported by other reporting manager(s).)



List of Other Managers Reporting for this Manager:

     Form 13F File Number            Name

     028-14367                       Two Sigma Advisers, LLC
    ---------------------           ---------------------------------------








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