The Energetic Gamma Ray Experiment Telescope (EGRET) on the Compton Gamma Ray Observatory has detected gamma rays from the Moon as it passed through the instrument field of view several times between 1991 and 1994. The average flux, and the energy spectrum of the lunar gamma radiation are consistent with a model of gamma ray production by cosmic ray interactions with the lunar surface, and the flux varies as expected with the solar cycle. Although the same processes may occur on the Sun, EGRET does not detect the quiet Sun. Thus, in high-energy gamma rays, the Moon is brighter than the quiet Sun.