Theoretical and empirical evidence indicates that competing species can coexist if dispersal, migration, and competitive interactions occur over relatively small spatial scales. In particular, spatial structure appears to be critical to certain communities with nontransitive competition. A typical nontransitive system involves three competing species that satisfy a relationship similar to the children's game of rock-paper-scissors. Although the ecological dynamics of nontransitive systems in spatially structured communities have received some attention, fewer studies have incorporated evolutionary change. Here we investigate evolution within toxic bacterial biofilms using an agent-based simulation that represents a nontransitive community containing three populations of Escherichia coli. In structured, nontransitive communities, strains evolve that do not maximize their competitive ability: They do not reduce their probability of death to a minimum or increase their toxicity to a maximum. That is, types evolve that exercise restraint. We show that nontransitivity and spatial structure (in the form of localized interactions) are both necessary for the evolution of restraint in these biofilms.