Female chimpanzees exhibit exceptionally slow rates of reproduction and raise their offspring without direct paternal care. Therefore, their reproductive success depends critically on long-term access to high-quality food resources over a long lifespan. Chimpanzee communities contain multiple adult males, multiple adult females and their offspring. Because males are philopatric and jointly defend the community range while most females transfer to new communities before breeding, adult females are typically surrounded by unrelated competitors. Communities are fission–fusion societies in which individuals spend time alone or in fluid subgroups, whose size depends mostly on the abundance and distribution of food. To varying extents in different populations, females avoid direct competition by foraging alone or in small groups in distinct, but overlapping core areas within the community range to which they show high fidelity. Although rates of aggression are low, females compete for space and access to food. High rank correlates with high reproductive success, and high-ranking females win direct contests for food and gain preferential access to resource-rich sites. Females are aggressive to immigrant females and even kill the newborn infants of community members. The intensity of such aggression correlates with population density. These patterns are compared to those in other species, including humans.