We study the kinetics of an irreversible monomer-monomer model of heterogeneous catalysis. In this model, two reactive species, A and B, adsorb and stick to single sites of a catalytic substrate. Surface reactions are assumed to occur only between dissimilar species that are nearest neighbors on the substrate. The kinetics of the process are studied in the reaction-controlled limit. We map the monomer-monomer model of heterogeneous catalysis onto a kinetic Ising model and find that the dynamics of the process is a superposition of zero-temperature spin-flip dynamics and infinite-temperature spin-exchange dynamics. We solve the kinetics analytically and determine the rate at which the catalyst becomes ``saturated,'' i.e., completely covered by only one species. We show that the saturation time is proportional to N ln(N), where N is the number of catalyst sites. We also discuss the monomer-monomer process with desorption.