We present X-ray/γ-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 X-ray spectra are well represented by a power law with a photon spectral index of Γ ≃ 1.75 and a Compton reflection component with a fluorescent Fe Kα line corresponding to a solid angle of an optically-thick, ionized, medium of ∼ 0.4×2π. The OSSE data ( 50 keV) 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 an optical depth of τ ∼ 1 and kT ≃ 50 keV. We also study the distance to the system and find it to be > ∼ 3 kpc, ruling out earlier determinations of ∼ 1 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.We find the data are incosistent 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 with the viscosity parameter of α ∼ 1 accreting at a rate close to the maximum set by advection. The hot disc is surrounded by a cold outer disc, which gives rise to the reflection component and a soft X-ray excess, also present in the data. The seed photons for Comptonization are unlikely to be due to thermal synchrotron radiation. Rather, they are supplied by the outer cold disc and/or cold clouds within the hot disc. e ± pair production is negligible if electrons are thermal. The hot disc model, which scaled parameters are independent of the blackhole 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 γ-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 > ∼ 50 keV represents a black-hole signature.