A particle-based Monte Carlo numerical method is developed for computation of flow in a low-thrust hydrogen arcjet. The method employs the direct simulation Monte Carlo technique to compute the nonequilibrium fluid mechanics and thermochemical relaxation. Simulation of plasma effects is included at a simple level that ensures charge neutrality. A new model is developed to include Ohmic heating in the simulation. Results are presented for a flow condition that has been studied experimentally with a number of different diagnostic techniques. A strong degree of thermal nonequilibrium is found in the flow. It is demonstrated that Ohmic heating is important, and that the Monte Carlo model captures the important physics very well. The predicted results are in very good agreement with most of the experimental data.