The nature of cold three-flavor quark matter at the large (but not asymptotic) densities relevant to neutron star phenomenology is not resolved. The gapless CFL phase, which was previously believed to have the lowest free energy, was recently shown to be unstable in the sense that some phase must have lower free energy. The nature of the instability motivates the hypothesis that the stable phase is a crystalline color superconductor. In this talk, which reports on work done in collaboration with Krishna Rajagopal, I will present the calculation of the free
energies of three-flavor crystalline color superconductors for realistic crystal structures in the Ginsburg-Landau approximation. All previous work on this subject neglected the strange quarks; we include them, with qualitative consequences. We calculate free energies for many crystal
structures, and find two (based upon cubic symmetry) that have lower free energy than the gapless CFL phase over the lower density half of the relevant parameter space.