A numerical study of the stability of the AB13 crystal structure in a mixture of dissimilar hard spheres is reported. This crystal structure has recently been observed by Bartlett and coworkers in experiments on suspensions of colloidal hard-sphere mixtures. We find that, over a range of densities and diameter ratios, the AB13 phase is thermodynamically stable both with respect to the fluid mixture and the crystal structures of pure A and pure B. A tentative phase diagram is presented.