Our closest nonhuman primate relatives, chimpanzees, engage in potentially lethal between-group conflict; this collective aggressive behavior shows parallels with human warfare. In some communities, chimpanzee males also severely attack and even kill females of the neighboring groups. This is surprising given their system of resource defense polygyny, where males are expected to acquire potential mates. We develop a simple mathematical model based on reproductive skew among primate males to solve this puzzle. The model predicts that it is advantageous for high-ranking males but not for low-ranking males to attack females. It also predicts that more males gain a benefit from attacking females as the community's reproductive skew decreases, i.e., as mating success is more evenly distributed. Thus, fatal attacks on females should be concentrated in communities with low reproductive skew. These attacks should also concur with between-community infanticide. A review of the chimpanzee literature provides enough preliminary support for this prediction to warrant more detailed testing.