In facultatively monogamous mammals, females are thought to be too widely dispersed for males to defend more than one female range. We tested this hypothesis in a monogamous antelope, Kirk's dik-dik, Madoqua kirkii. Dik-dik territories were compared across three indices of quality to investigate whether males are monogamous because of constraints on the area, or resources, that they are capable of defending. Territories varied substantially in size and quality, with some containing up to five times the resources of others. Moreover, the territories of four temporarily polygynous males were not of higher quality than those of monogamous males. These results are inconsistent with the idea that dik-diks are facultatively monogamous: males can, and often do, defend enough resources and sufficient area to support two or more females. We investigated the relationship between resource dispersion and monogamy further by providing food to territories over a 3-month period. Although provisioned pairs obtained 20% of their daily requirements from the food, there was no change in the territory size of either sex. Female dispersion does not account for monogamy in the dik-dik; instead we argue that monogamy has evolved as a result of male mate guarding.