Periodic, photometric variations with a full amplitude of about 0.2 mag have been discovered in the X-ray nova A0620-00 in its quiescent state. The most probable period is 7.8 hr, although there are several additional candidate periods. The broad-band (4000-6400 A) observations were made on six consecutive nights in October-November 1981 with the 1.3 m McGraw-Hill telescope and the MIT CCD system (MASCOT). It is possible that the light curve is due to ellipsoidal variations of the K dwarf caused by the tidal forces of the neutron star. If so, the relatively large amplitude implies that the K dwarf fills a substantial fraction of its Roche lobe and that the orbital inclination of the system is large. It is also possible that the light curve is due to an eclipse in which the two light sources are the K dwarf and the accretion disk.