Keeping Faith With the Greatest Generation Military Retirees Act of 2010 - Amends title XVIII (Medicare) of the Social Security Act to waive the monthly part B premium (Supplementary Medical Insurance Benefits for the Aged and Disabled) with respect to: (1) an individual who is entitled to military retired or retainer pay based upon service that began before December 7, 1956; and (2) the spouse, widow, or widower of such individuals.