All stellar-mass black holes have hitherto been identified by X-rays emitted from gas that is accreting onto the black hole from a companion star. These systems are all binaries with a black-hole mass that is less than 30 times that of the Sun^1–4. Theory predicts, however, that X-ray-emitting systems form a minority of the total population of star–black-hole binaries^5,6. When the black hole is not accreting gas, it can be found through radial-velocity measurements of the motion of the companion star. Here we report radial-velocity measurements taken over two years of the Galactic B-type star, LB-1. We find that the motion of the B star and an accompanying Hα emission line require the presence of a dark companion with a mass of 68−13+11 solar masses, which can only be a black hole. The long orbital period of 78.9 days shows that this is a wide binary system. Gravitational-wave experiments have detected black holes of similar mass, but the formation of such massive ones in a high-metallicity environment would be extremely challenging within current stellar evolution theories.