We report 77Se NMR data in the normal and superconducting states of a single crystal of FeSe for several different field orientations. The Knight shift is suppressed in the superconducting state for in-plane fields, but does not vanish at zero temperature. For fields oriented out of the plane, little or no reduction is observed below Tc. These results reflect spin-singlet pairing emerging from a nematic state with large orbital susceptibility and spin-orbit coupling. The spectra and spin-relaxation rate data reveal electronic inhomogeneity that is enhanced in the superconducting state, possibly arising from enhanced density of states in the vortex cores. Despite the spin polarization of these states, there is no evidence for antiferromagnetic fluctuations.