We present a direct calculation by molecular-dynamics computer simulation of the crystal/melt interfacial free energy gamma for a system of hard spheres of diameter sigma. The calculation is performed by thermodynamic integration along a reversible path defined by cleaving, using specially constructed movable hard-sphere walls, separate bulk crystal, and fluid systems, which are then merged to form an interface. We find the interfacial free energy to be slightly anisotropic with gamma = 0.62+/-0.01, 0.64+/-0.01, and 0. 58+/-0.01k(B)T/sigma(2) for the (100), (110), and (111) fcc crystal/fluid interfaces, respectively. These values are consistent with earlier density functional calculations and recent experiments.