Competitive exclusion – n species cannot coexist on fewer than n limiting resources in a constant and isolated environment – has been a central ecological principle for the past century. Coexistence in natural communities and even in simple microcosms would seem to belie such a principle. Nevertheless, because competitive exclusion has been substantiated by some influential empirical and theoretical studies, most ecologists have accepted it as a principle and devoted substantial effort to find mechanisms explaining coexistence of competing species. As with empirical studies, mathematical proofs do not universally demonstrate exclusion. Many biologically sensible models with density-dependent per capita growth rates allow competitive coexistence. Here we show that, when consumer-resource dynamics are solely governed by statistical mechanics, arguably the most parsimonious, fundamental driving force for the dynamics of a system, coexistence emerges as the norm rather than the exception. Any number of species can coexist on a single resource in a constant, isolated environment. Moreover species tend to coexist at constant relative abundances irrespective of variation in the abundance of the total community or the resource. Depending on species characteristics, competition can cause rarity, which may subsequently lead to extinction in small populations due to stochastic mortality events. However, our model shows that ecological similarity does not lead to rarity; on the contrary, the more similar species are, the more even their proportions will be. Thus limiting similarity in the niches of species is not required to explain coexistence.