Using a spatially explicit cellular automaton model with local competition, we investigate the potential for varied levels of competitive intransitivity (i.e., nonhierarchical competition) to promote species coexistence. As predicted, on average, increased levels of intransitivity result in more sustained coexistence within simulated communities, although the outcome of competition also becomes increasingly unpredictable. Interestingly, even a moderate degree of intransitivity within a community can promote coexistence, in terms of both the length of time until the first competitive exclusion and the number of species remaining in the community after 500 simulated generations. These results suggest that modest levels of intransitivity in nature, such as those that are thought to be characteristic of plant communities, can contribute to coexistence and, therefore, community-scale biodiversity. We explore a potential connection between competitive intransitivity and neutral theory, whereby competitive intransitivity may represent an important mechanism for "ecological equivalence."