In three permanent inventory plots comprising 12.4 ha of undisturbed forest at La Selva, Costa Rica, all stems ≥10 cm dbh were mapped and identified to species. There were 1628, 1478 and 1954 trees in the plots, representing 168, 166 and 171 species respectively. We determined the species of each nearest-neighbor pair of trees, and asked whether the occurrence of species pairs conforms to a simple random mixing model. If trees are randomly mixed in terms of species, the expected frequency of any nearest neighbor species combination is a function of the relative abundance of the two species. Departures from random mixing could arise from species interactions, differential responses to habitat, or both. The number of possible ij species combinations increases approximately as the square of the number of species. For the 168 species in plot 1, for example, there are 14 196 possible combinations. We compared the expected frequency of each species combination in the three plots (42 736 combinations in all) with observed frequencies. Over 98% of the combinations had observed frequencies of zero and expected frequencies close to zero. A consequence of high diversity is low density of most individual species, and exceedingly low frequencies of the vast majority of species combinations. For each of the 805 combinations with observed frequencies >0, we used simulation to generate a distribution of expected frequencies. We used a t-test to compare the observed frequency with the mean of the simulated distribution for each combination. Only 40 combinations (0.09% of the possible species combinations in the plots) departed from expected frequencies; 39 combinations were more common, and one less common than expected. The overwhelming majority of nearest neighbor species combinations occur at frequencies predictable from their individual abundances.