Exhibit 32.1

                        CERTIFICATION OF PERIODIC REPORT

I, John D. Finnegan, Chairman, President and Chief Executive Officer of The
Chubb Corporation (the "Corporation"), certify, pursuant to 18 U.S.C. Section
1350 adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

       (1) the Quarterly Report on Form 10-Q of the Corporation for the
           quarterly period ended June 30, 2004 (the "Report") fully complies
           with the requirements of Section 13(a) or 15(d) of the Securities
           Exchange Act of 1934 (15 U.S.C. 78m or 78o(d)); and

       (2) the information contained in the Report fairly presents, in all
           material respects, the financial condition and results of operations
           of the Corporation.

Dated: August 6, 2004


/s/ John D. Finnegan
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John D. Finnegan
Chairman, President and Chief Executive Officer