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 ± 6·10 – 5kTs2, where s 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.