The final evolution of a binary-black-hole system gives rise to a recoil velocity if an asymmetry is present in the emitted gravitational radiation. Measurements of this effect for nonspinning binaries with unequal masses have pointed out that kick velocities approximately 175 km/s can be reached for a mass ratio approximately 0.36. However, a larger recoil can be obtained for equal-mass binaries if the asymmetry is provided by the spins. Using two independent methods we show that the merger of such binaries yields velocities as large as approximately 440 km/s for black holes having unequal spins that are antialigned and parallel to the orbital angular momentum.