Binarity is believed to dramatically affect the history and geometry of mass loss in AGB and post-AGB stars, but observational evidence of binarity is sorely lacking. As part of a project to look for hot binary companions to cool AGB stars using the GALEX archive, we have discovered a late-M star, Y Gem, to be a source of strong and variable UV emission. Y Gem is a prime example of the success of our technique of UV imaging of AGB stars in order to search for binary companions. Y Gem's large and variable UV flux makes it one of the most prominent examples of a late AGB star with a mass accreting binary companion. The UV emission is most likely due to emission associated with accretion activity and a disk around a main-sequence companion star. The physical mechanism generating the UV emission is extremely energetic, with an integrated luminosity of a few L(sun) at its peak. We also find weak CO J=2-1 emission from Y Gem with a very narrow line profile (FWHM of 3.4 km/s). Such a narrow line is unlikely to arise in an outflow, and is consistent with emission from an orbiting, molecular reservoir of radius 300 AU. Y Gem may be the progenitor of the class of post-AGB stars which are binaries and possess disks but no outflows.