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. Theory predicts, however, that X-ray-emitting systems form a minority of the total population of star–black-hole binaries. When the black hole is not accreting gas, it can be found through radial-velocity measurements of the motion of the companion star. We report here radial-velocity measurements taken over two years of the Galactic B-type star, LB-1. The star was initially discovered during a monitoring campaign with the 4-m telescope LAMOST and subsequently studied in more detail with the 10-m class telescopes GTC and Keck.  We find that the motion of the B star and a superimposed Hα emission line (see figure) require the presence of a dark companion with a mass of 68 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. For comparison, black holes detected in X-ray binaries have masses in the range 5-15 solar masses. On the other hand, gravitational-wave experiments have detected black holes with several tens of solar masses. However, the formation of a ~70 solar mass black hole in a high-metallicity environment is extremely challenging within current stellar evolution theories. This would require a significant reduction in wind mass-loss rates and overcoming the pair-instability supernova phase, which limits the maximum black hole mass to less than ~50 solar masses. Alternatively, the black hole in LB-1 might have formed after a binary black hole merger or other exotic mechanisms.