Hybrid quantum devices, in which dissimilar quantum systems are combined in order to attain qualities not available with either system alone, may enable far-reaching control in quantum measurement, sensing, and information processing. A paradigmatic example is trapped ultracold atoms, which offer excellent quantum coherent properties, coupled to nanoscale solid-state systems, which allow for strong interactions. We demonstrate a deterministic interface between a single trapped rubidium atom and a nanoscale photonic crystal cavity. Precise control over the atom's position allows us to probe the cavity near-field with a resolution below the diffraction limit and to observe large atom-photon coupling. This approach may enable the realization of integrated, strongly coupled quantum nano-optical circuits.