A new chemistry model is developed for the direct simulation Monte Carlo method (DSMC). This model explicitly includes separate biasing of the reaction cross section to the translational, rotational, and vibrational energies of each collision. The multiple parameter model is calibrated using detailed information on the formation of nitric oxide based on quasi-classical trajectory calculations. The trajectory analysis provides reaction cross sections, and the energy distributions of reactants and products. In the DSMC approach, product energies are assigned by the widely used Borgnakke-Larsen approach. The performance of the new DSMC model is evaluated in terms of reaction cross sections, energy distributions of reacting molecules, energy distributions of nitric oxide molecules formed in the reaction, and overall reaction rate coefficient. In all cases, the new chemistry model gives favorable agreement with the trajectory calculations. The excellent agreement obtained for product energy distributions indicates that the simple Borgnakke-Larsen energy partitioning scheme is a valid approach for this reaction. The new Monte Carlo chemistry model is applied to a hypersonic, low-density, reacting flow of air. By comparison with a previous chemistry model, the new model predicts significantly higher concentrations of mine oxide. It is also found that nitric oxide molecules are formed in highly nonequilibrium states. Both of these findings are supported by experimental observations.