The Gamma Ray Spectrometer (GRS) on the Solar Maximum Mission satellite (SMM) has observed a strong Galactic source of 511 keV annihilation radiation from its launch in 1980 to its reentry in 1989. These observations are consistent with an extended source having an intensity of about 0.002 gamma/sq cm/s averaged over the central radian of Galactic longitude. These data are searched for evidence of the variable Galactic center source of 511 keV line radiation which was reported to have reappeared in 1988 by Leventhal et al. The SMM data are consistent with, but do not require, a compact source emitting a time-averaged flux of about 0.0004 gamma/sq cm/s during about 3 month transits in 1987 and 1988; they are inconsistent with a compact source flux in excess of 0.0008 gamma/sq cm/s for each year.