In pair-living mammals, genetic monogamy is extremely rare. One possible reason is that in socially monogamous animals, mate choice can be severely constrained, generating a risk of incest or incompatibility between partners. To escape these constraints and minimize inbreeding, individuals might engage in extra-pair copulations. Alternatively, inbreeding can be avoided by natal dispersal. However, little is known about the interactions between mating system, mate choice and dispersal in pair-living mammals. Here we show that coppery titi monkeys (Plecturocebus cupreus), despite exhibiting no relatedness- or heterozygosity-based mate choice, are genetically monogamous and have low relatedness between pair mates. We further found that dispersal was opportunistic and often local. This indicates that even random dispersal can generate sufficient genetic diversity to prevent inbreeding, rendering active mate choice unnecessary. Our findings demonstrate that sufficient level of dispersal, together with limited opportunities for extra-pair copulations, can facilitate the evolution of genetic monogamy.