The paper discusses some aspects of a parallel, dynamic Monte Carlo (MC) simulation of a chemical surface reaction. First a previously unpublished sequential algorithm is given. Then a domain decomposition is applied in order to obtain a parallel algorithm. This algorithm has been implemented for the Ziff model of CO oxidation over a Platinum surface. Simulations have been done on two MIMD platforms, a 50 node Transputer system and a 4 node PowerXplorer system. The results of these simulations are compared to results found in the literature. The performance is compared to that of the sequential algorithm and for the Transputer implementation the scaling behaviour is discussed. The case study shows that the domain decomposition approach is a viable one. It also shows that more research is required in order to make firm, quantitative statements about its correctness.