The realization of efficient optical interfaces for solid-state atom-like systems is an important problem in quantum science with potential applications in quantum communications and quantum information processing. We describe and demonstrate a technique for coupling single nitrogen vacancy (NV) centers to suspended diamond photonic crystal cavities with quality factors up to 6000. Specifically, we present an enhancement of the NV center's zero-phonon line fluorescence by a factor of ~ 7 in low-temperature measurements.