All organisms, especially terrestrial plants and other sessile species, interact mainly with their neighbors, but neighborhoods can differ in composition because of dispersal and mortality. There is increasingly strong evidence that the spatial structure created by these forces profoundly influences the dynamics, composition, and biodiversity of communities. Nonspatial models predict that no more consumer species can coexist at equilibrium than there are limiting resources. In contrast, a similar model that includes neighborhood competition and random dispersal among sites predicts stable coexistence of a potentially unlimited number of species on a single resource. Coexistence occurs because species with sufficiently high dispersal rates persist in sites not occupied by superior competitors. Coexistence requires limiting similarity and two—way or three—way interspecific trade—offs among competitive ability, colonization ability, and longevity. This spatial competition hypothesis seems to explain the coexistence of the numerous plant species that compete for a single limiting resource in the grasslands of Cedar Creek Natural History Area. It provides a testable, alternative explanation for other high diversity communities, such as tropical forests. The model can be tested (1) by determining if coexisting species have the requisite trade—offs in colonization, competition, and longevity, (2) by addition of propagules of propagules to determine if local species abundances are limited by dispersal, and (3) by comparisons of the effects on biodiversity of high rates of propagule addition for species that differ in competitive ability.