THE X-ray transient source GS2023 + 338 was discovered in outburst by the Ginga satellite in 1989 (ref. 1) and has since been identified with the previously known recurrent nova V404 Cygni 2. This system is recognized to be a low-mass X-ray binary 3, with X-ray behaviour similar to black hole systems 4, but attempts to deduce an orbital period from photometry 5-9 and spectroscopy 10,11 have yielded modulations with periods from 10 minutes to 6 hours. Two years after the outburst, we have used the William Herschel Telescope to find absorption features in V404 Cyg characteristic of a late G or early K star with a radial velocity curve of amplitude 211 +/- 4 km s-1 and period 6.473 +/- 0.001 days. The deduced mass function of 6.26 +/- 0.31 M. is a firm lower limit to the mass of the compact object, which for reasonable assumptions of orbital inclination and companion star mass must be a black hole with probable mass in the range 8-15.5 M.. We consider this the most persuasive case yet for the existence of a black hole.