Globular star clusters contain thousands to millions of old stars packed within a region only tens of light years across. Their high stellar densities make it very probable that their member stars will interact or collide. There has accordingly been considerable debate about whether black holes should exist in these star clusters. Some theoretical work suggests that dynamical processes in the densest inner regions of globular clusters may lead to the formation of black holes of ~1,000 solar masses. Other numerical simulations instead predict that stellar interactions will eject most or all of the black holes that form in globular clusters. Here we report the X-ray signature of an accreting black hole in a globular cluster associated with the giant elliptical galaxy NGC 4472 (in the Virgo cluster). This object has an X-ray luminosity of about 4×1039ergs-1, which rules out any object other than a black hole in such an old stellar population. The X-ray luminosity varies by a factor of seven in a few hours, which excludes the possibility that the object is several neutron stars superposed.