Numerous grassland experiments have found evidence for a complementarity effect, an increase in productivity with higher plant species richness due to niche partitioning. However, empirical tests of complementarity in natural forests are rare. We conducted a spatially explicit analysis of 518 433 growth records for 274 species from a 50‐ha tropical forest plot to test neighborhood complementarity, the idea that a tree grows faster when it is surrounded by more dissimilar neighbors. We found evidence for complementarity: focal tree growth rates increased by 39.8% and 34.2% with a doubling of neighborhood multi‐trait dissimilarity and phylogenetic dissimilarity, respectively. Dissimilarity from neighbors in maximum height had the most important effect on tree growth among the six traits examined, and indeed, its effect trended much larger than that of the multi‐trait dissimilarity index. Neighborhood complementarity effects were strongest for light‐demanding species, and decreased in importance with increasing shade tolerance of the focal individuals. Simulations demonstrated that the observed neighborhood complementarities were sufficient to produce positive stand‐level biodiversity–productivity relationships. We conclude that neighborhood complementarity is important for productivity in this tropical forest, and that scaling down to individual‐level processes can advance our understanding of the mechanisms underlying stand‐level biodiversity–productivity relationships.