  We present X-ray/gamma-ray spectra of the binary GX 339-4 observed in the
hard state simultaneously by Ginga and CGRO OSSE during an outburst in 1991
September. The Ginga spectra are well represented by a power law with a photon
spectral index of 1.75 and a moderately-strong Compton reflection component
with a fluorescent Fe K alpha line. The OSSE data require a sharp high-energy
cutoff in the power-law spectrum. The broad-band spectra are very well modelled
by repeated Compton scattering in a thermal plasma with tau=1 and kT=50 keV. We
also find the distance to the system to be > 3 kpc, ruling out earlier
determinations of 1.3 kpc. Using this limit, the observed reddening and the
orbital period, we find the allowed range of the mass of the primary is
consistent with it being a black hole. The data are inconsistent with models of
either homogenous or patchy coronae above the surface of an accretion disc.
Rather, they are consistent with the presence of a hot inner hot disc accreting
at a rate close to the maximum set by advection and surrounded by a cold outer
disc. The seed photons for Comptonization are supplied by the outer cold disc
and/or cold clouds within the hot disc. Pair production is negligible if
electrons are thermal. The hot disc model, which scaled parameters are
independent of the black-hole mass, is supported by the similarity of the
spectrum of GX 339-4 to those of other black-hole binaries and Seyfert 1s. On
the other hand, their spectra in the soft gamma-ray regime are significantly
harder than those of weakly-magnetized neutron stars. Based on this difference,
we propose that the presence of broad-band spectra corresponding to thermal
Comptonization with kT of 50 keV or more represents a black-hole signature.
