A new application of the replica exchange technique is demonstrated for use in reactive Monte Carlo simulations. The technique allows the system to traverse barriers in the free energy landscape through configuration swaps of higher temperature replicas, replicas with scaled potential energy parameters, or replicas existing at modified values of the reaction driving force (free energy of reaction). Acceptance rules are developed for the swap moves among the replicas, and the application of the replica exchange method is shown to be straightforward. We demonstrate the accuracy and efficiency of this technique by simulating the conversion of a model reaction. We find large increases in efficiency when performing simulations at computationally challenging conditions, such as high densities, particularly when a pre-converged configuration reservoir is incorporated. With minimal effort, it should be possible to extend this replica exchange approach to systems involving multiple simultaneous reactions and to systems with more complex multi-site reacting species.