More than 100 reactions between stable molecules and free radicals have been shown to remain rapid at low temperatures. In contrast, reactions between two unstable radicals have received much less attention due to the added complexity of producing and measuring excess radical concentrations. We performed kinetic experiments on the barrierless N((4)S) + OH((2)Pi) -> H((2)S) + NO((2)Pi) reaction in a supersonic flow (Laval nozzle) reactor. We used a microwave-discharge method to generate atomic nitrogen and a relative-rate method to follow the reaction kinetics. The measured rates agreed well with the results of exact and approximate quantum mechanical calculations. These results also provide insight into the gas-phase formation mechanisms of molecular nitrogen in interstellar clouds.