The first Zeldovich reaction, N2 + O → NO + N, plays a major role in nitric oxide formation in reentry flows, combustion, and discharge flow systems. The kinetics of this reaction is uncertain under the strong thermodynamic nonequilibrium conditions and extremely high temperatures that often characterize these flows. We assess the influence of these conditions on the reaction rate using detailed quasiclassical trajectory calculations on the 3A″ surface obtained from ab initio contracted configuration interaction data. The effect of reactant energy modes on the rate constant is analyzed and a functional dependence of the rate constant on the vibrational, rotational, and translational temperatures is obtained. It is seen that strong nonequilibrium can reduce the rate constant by a factor of 5-6. In addition, the energy of the NO molecules formed by this reaction is determined and its dependence on the reagent energy is studied. The vibrational and rotational distributions of the product NO molecules under typical re-entry flow conditions are obtained and are found to be nearly Boltzmann. For strong nonequilibrium cases, NO is formed at high vibrational and rotational temperatures, in accordance with the bow-shock ultraviolet flight experiments.