We estimate the rate at which randomly stacked hard-sphere crystals transform into the thermodynamically stable face-centered cubic phase. As an input for this estimate we need both the free-energy difference between bulk face-centered cubic (fcc) and hexagonal close packed (hcp) phases, and the hcp-fcc interfacial free energy. The latter quantity was computed using a lattice-switch Monte Carlo (MC) simulation method. We find the interfacial free energy to be nonzero but extremely small: 26 +/- 6.1(05)kT/sigma(2),where sigma is the particle diameter. The free energy difference between the bulk phases was calculated using two different techniques. On the basis of our simulation results we estimate that in hard-sphere colloidal suspensions millimeter-sized randomly stacked crystal will anneal to form essentially pure fcc crystal on a time scale of months to years.