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 X-ray spectra are well represented by a power law with a photon spectral index of \Gamma \simeq 1.75 and a Compton reflection component with a fluorescent Fe K \alpha line corresponding to a solid angle of an optically-thick , ionized , medium of \sim 0.4 \times 2 \pi . The OSSE data ( \geq 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 \tau \sim 1 and kT \simeq 50 keV . We also study the distance to the system and find it to be \ga 3 kpc , ruling out earlier determinations of \sim 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 \alpha \sim 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 ^ { \pm } 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 \ga 50 keV represents a black-hole signature .