A new dissociation model for the direct simulation Monte Carlo (DSMC) method is formulated using the threshold line concept. This model considers in some detail the coupling between the vibrational energy distribution of molecules in a gas and the rate of dissociation. For a particular reaction, the new threshold line model only requires determination of a leading multiplicative constant and is therefore significantly less deterministic than existing DSMC chemistry models. The new model is evaluated in a heat bath under equilibrium and nonequilibrium conditions. It is also employed to calculate hypersonic shock waves of nitrogen and air. Comparison of the results generated with the new model is made with existing experimental data and with previous computational results. The more detailed DSMC implementation reveals properties of the threshold line dissociation model not apparent in the previous continuum implementation.