Unstable Be-7 (half-life 53.28 days) is expected to be present in the ejecta of classical novae. If the frequency of novae in the central Galaxy is high enough, a nearly steady state abundance of Be-7 will be present there. Data accumulated during transits of the Galactic center across the aperture of the Solar Maximum Mission Gamma Ray Spectrometer have been searched for evidence of the 478 keV gamma-ray line resulting from Be-7 decay. A 3-sigma upper limit of 0.00016 gamma/sq cm s has been placed on the emission in this line from the central radian of the Galactic plane. Less stringent limits have been set on the production of Be-7 in Nova Aquilae 1982, Nova Vulpeculae 1984 No. 2, and Nova Centauri 1986 from observations with the same instrument.