Resonantly enhanced multi-photon ionization (REMPI) laser spectroscopic and molecular beam-surface scattering techniques are coupled to study the rotationally inelastic scattering of N₂ from Au(111). The scattered N₂ rotational distributions are markedly non-Boltzmann and exhibit pronounced maxima at large angular momentum transfers ( Delta J=20 to 30). These maxima are indicative of direct rotational rainbow scattering and strongly depend upon the translational energy of the incident N₂ molecular beam. The translational energy dependence of the rainbow rotational energy yeilds a value of 4.1 kcal mol^-1 for the depth of the laterally averaged N₂-Au(111) physisorption potential.