Microbes can engage in social interactions ranging from cooperation to warfare. Biofilms are structured, cooperative microbial communities. Like all cooperative communities, they are susceptible to invasion by selfish individuals who benefit without contributing. However, biofilms are pervasive and ancient, representing the first fossilized life. One hypothesis for the stability of biofilms is spatial structure: segregated patches of related cooperative cells are able to outcompete unrelated cells. These dynamics have been explored computationally and in bacteria; however, their relevance to eukaryotic microbes remains an open question. The complexity of eukaryotic cell signaling and communication suggests the possibility of different social dynamics. Using the tractable model yeast, Saccharomyces cerevisiae, which can form biofilms, we investigate the interactions of environmental isolates with different social phenotypes. We find that biofilm strains spatially exclude non-biofilm strains, and that biofilm spatial structure confers a consistent and robust fitness advantage in direct competition. Furthermore, biofilms may protect against killer toxin, a warfare phenotype. During biofilm formation, cells are susceptible to toxin from nearby competitors; however, increased spatial use may provide an escape from toxin-producers. Our results suggest that yeast biofilms represent a competitive strategy, and that principles elucidated for the evolution and stability of bacterial biofilms may apply to more complex eukaryotes.