X-RAY novae are binary systems in which a compact object accretes gas from a companion star. In several cases there is good evidence that the compact object is a black hole(1-5). The best evidence for the presence of a black hole comes from measuring the orbital velocity of the companion star and thereby determining the minimum mass of the compact object; when this mass exceeds the maximum mass for a neutron star (less than or similar to 3 solar masses(6)), a black hole seems the only remaining possibility. The unusual X-ray nova GRO J1655 - 40 (refs 7-10) is unique because it emits superluminal radio jets, suggesting that it is a low-luminosity counterpart to active galactic nuclei(7,9), which are thought to be powered by accretion onto a massive black hole. Here we report observations of the optical counterpart(10) of GRO J1655 - 40, which show that the system undergoes periodic eclipses; the edge-on geometry thus implied allows a determination of the companion star’s true velocity. The mass of the compact object derived from the velocity curve is at least 3.16+/-0.15 solar masses, which strongly supports its identification as a black hole.