The Oriented Scintillation Spectrometer Experiment (OSSE) on the Compton Gamma Ray Observatory observed the Galactic black hole candidate GX 339-4 as a target of opportunity in 1991 September, in response to the outburst reported by BATSE. We report here on energy spectra in the 50 keV-10 MeV range obtained by OSSE. The source was detected from 50 to 400 keV at a level relative to the Crab Nebula of similar to 30%. The observed spectrum was described reasonably well by a power law with an exponential cutoff; a least-squares fit yielded a photon index of 0.88 +/- 0.05 and a cutoff energy of 68 +/- 2 keV. The addition of a Compton reflection component did not significantly improve the overall fit. An optically thin thermal bremsstrahlung spectrum also provides a good fit, and the thermal Comptonization model of Sunyaev & Titarchuk, while deficient in describing the data above similar to 200 keV, cannot formally be ruled out. A pure power law with reflection does not fit the observed spectrum. During a follow-up observation made in 1991 November, the intensity of the source below 100 keV had dropped by more than a factor of 40, and it was no longer detected above similar to 100 keV. The energy spectrum during the November observation could be characterized by a power law with a photon index of 2.3 +/- 0.3; the spectrum was fitted equally well with the same exponentially cutoff power-law model applied to the September observation, reduced in intensity by a factor of similar to 40. During the 1991 September observation, the luminosity in the 50-400 keV band was approximately 2 x 10(37) ergs s(-1) (assuming a distance of 4 kpc), no more than a factor of 5 below the soft X-ray luminosity of GX 339-4 observed in its X-ray high state. The luminosity during the 1991 November observation was similar to 5 x 10(35) ergs s(-1). Extrapolations of both the exponentially cutoff power-law and Sunyaev-Titarchuk models to the similar to 5-20 keV X-ray band yield flux levels very close to that observed by Ginga during an overlapping interval in 1991 September, when GX 339-4 was reported to be in its low X-ray state. This may be one of the strongest indications to date of a direct correspondence between the low X-ray state and gamma-ray outbursts of GX 339-4.