EXHIBIT (b)

Certification of CEO and CFO Pursuant to

18 U.S.C. Section 1350,

as Adopted Pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

In connection with the Report on Form N-CSR of Guggenheim Enhanced Equity Income Fund (the “Company”) for the period ended December 31, 2010 (the “Report”), Kevin M. Robinson, as Chief Executive Officer and Chief Legal Officer of the Company, and Bruce Albelda, as Interim Chief Financial Officer, Interim Chief Accounting Officer and Interim Treasurer of the Company, each hereby certifies, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to the best of his knowledge:

(1)   the Report fully complies with the requirements of Section 13 (a) or 15 (d) of the Securities Exchange Act of 1934; and

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

Dated:  March 9, 2011                                                     

                      /s/ Kevin M. Robinson                         

Name:           Kevin M. Robinson

Title:             Chief Executive Officer and Chief Legal Officer

                      /s/ Bruce Albelda                                   

Name:           Bruce Albelda

Title:             Interim Chief Financial Officer, Interim Chief Accounting Officer and Interim Treasurer.