The University of California, San Diego (UCSD)/MIT hard X-ray and gamma-ray instrument on the HEAO 1 surveyed the region near the Galactic center 3 times during its lifetime in 1977-1979. During the 1977 September-October scan, a gamma-ray source was detected south of the Galactic center. The source was below the threshold sensitivity in the spring and fall of 1978. The source was detected with the medium energy phoswich scintillation counters which operated over the 80 keV-2 MeV range, had an area of 42 sq cm each, and a 17 deg FWHM aperture. The error box for the source is centered on l = 2.4 deg, b = -12.2 deg, with a 90% confidence error circle of approximately 3.5 deg radius. The flux in the 333-635 keV range was (1.89 +/- 0.29) x 10(exp -5) photons/(sq cm s keV) and was constant within statistics during the 1 month period the source was in the field of view. The spectrum can be characterized as a Gaussian in the range 300 less than or = E less than or = 650 keV, with a FWHM of 249 +/- 51 keV centered on 461 +/- 22 keV. The flux of this broad Gaussian is (6.6 +/- 1.1) x 10(exp -3) photons/(sq cm s). The source is tentatively identified with the 5.57 hr period low-mass X-ray-emitting binary system 1H 1822-371. Assuming this is correct, the ratio of gamma-ray to X-ray luminosity during the outburst was about 5; at a distance of 8 kpc, the gamma ray luminosity is 4 x 10(exp 37) ergs. The emission may be interpreted as a positron-pair plasma ejected from a compact object, possibly a black hole, and annihilating in a thick accretion disk surrounding the object.