The ability of humans to communicate via language is a complex, adapted phenotype, which undoubtedly has a recently evolved genetic component. However, the evolutionary dynamics of language-associated alleles are poorly understood. To improve our knowledge of such systems, a population-genetics model for language-associated genes is developed. (The model is general and applicable to social interactions other than communication.) When an allele arises that potentially improves the ability of individuals to communicate, it will experience positive frequency-dependent selection because its fitness will depend on how many other individuals communicate the same way. Consequently, new and rare alleles are selected against, posing a problem for the evolutionary origin of language. However, the model shows that if individuals form language-based cliques, then novel language-associated alleles can sweep through a population. Thus, the origin of language ability can be sufficiently explained by Darwinian processes operating on genetic diversity in a finite population of human ancestors.