NaOsO3 hosts a rare manifestation of a metal-insulator transition driven by magnetic correlations, placing the magnetic exchange interactions in a central role. We use resonant inelastic x-ray scattering to directly probe these magnetic exchange interactions. A dispersive and strongly gapped (58 meV) excitation is observed, indicating appreciable spin-orbit coupling in this 5d(3) system. The excitation is well described within a minimal model Hamiltonian with strong anisotropy and Heisenberg exchange (J(1) = J(2) = 13.9 meV). The observed behavior places NaOsO3 on the boundary between localized and itinerant magnetism.