Cygnus X-l, a strong X-ray source in a binary star system, is generally considered a good candidate for a black hole1. Its X-ray emission provides the best method of studying the physical processes near the collapsed object. The average energy spectrum (in the `low' state) is remarkably stable2 and has been interpreted as the result of comptonization, that is Compton scattering of optical or UV photons in a very hot plasma3-5. We have measured the low-state spectrum on 26 October to 18 November 1977, over a wide energy range (3 keV-8 MeV). This is the first measurement to cover such a broad energy range and the first long-term average measurement above 300 keV. This spectrum agrees well with a single temperature comptonization model at low energy, but shows a significant excess at high energy (E>300 keV).