Invasion of ecosystems by woody alien plant species is a widespread phenomenon. Interspecific competition has often been suggested as a mechanism for replacement of one species by another, but this is rarely tested. We investigated the potential of an invasive alien tree to transform vegetation by quantifying the relative abilities of the alien tree Schinus molle and dominant native trees Acacia tortilis and Rhus lancea to compete for light when growing in association within a South African semi-arid savanna. Due to dispersal of its fruits by birds, seedlings of S. molle establish under tree canopies. Using canopy symmetry as an index of ability to compete for light, we found that the alien S. molle consistently out-competes the dominant native tree species. The results also show that pod production of A. tortilis was higher when it grew alone compared to when it grew with S. molle or R. lancea. The percentage of dead branches was higher on A. tortilis trees growing in association with the S. molle. The outcome is that the alien tree will gradually increase in abundance, changing woodland structure and ecosystem processes. Our findings provide evidence for the role of competition in the process of alien plant invasions. We suggest that S. molle, previously considered a benign naturalized species in South Africa, should be declared a noxious weed in some parts of that country.