Territorial social species, including humans, compete between groups over key resources. This between-group competition has evolutionary implications on adaptations like in-group cooperation even with non-kin. An emergent property of between-group competition is group dominance. Mechanisms of group dominance in wild animal populations are difficult to study, as they require long-term data on several groups within a population. Here, using long-term data on four neighbouring groups of wild western chimpanzees, we test the hypothesis that group dominance impacts the costs and benefits of between-group competition, measured by territory size and the pressure exerted by neighbouring groups. Larger groups had larger territories and suffered less neighbour pressure compared with smaller groups. Within-group increase in the number of males led to territory increase, suggesting the role of males in territory acquisition. However, variation in territory sizes and neighbour pressure was better explained by group size. This suggests that the bisexually-bonded social system of western chimpanzees, where females participate in territorial behaviour, confers a competitive advantage to larger groups and that group dominance acts through group size in this population. Considering variation in social systems offers new insights on how group dominance acts in territorial species and its evolutionary implications on within-group cooperation.