Understanding the evolution and maintenance of social behaviour requires a better understanding of the physiological mechanisms underlying the trade-offs between the benefits and costs of social status. Social dominance is expected to provide advantages in terms of access to resources and to reproduction but acquiring and maintaining dominance may also entail physiological costs. Dominant individuals are likely to engage more frequently in aggressive behaviours and/or may allocate a substantial amount of energy and resources to signal their status. Hence, dominance is likely to involve multiple physiological processes that stimulate aerobic metabolism and lead to the generation of reactive oxygen species (ROS). When not depleted, ROS can ultimately lead to oxidative stress. However, the relationship between oxidative status and dominance has seldom been investigated. Here, we examined whether there is a physiological cost, measured as oxidative stress, associated with dominance in a highly social and cooperative bird, the sociable weaver, Philetairus socius. Oxidative status was assessed by measuring circulating oxidative damage and the plasma nonspecific antioxidant capacity. We found that in females, but not in males, dominance was associated with higher levels of oxidative damage than in same-sex subordinates, suggesting that the physiological cost of dominance is underpinned by oxidative stress in a sex-specific manner. This associated cost of dominance was independent of previous and future reproductive status. The sex difference in oxidative damage was associated with sex-specific differences in antioxidant defences, with males (the dominant sex) showing higher antioxidant levels than females, independently of their social rank. These findings indicate that social dominance may entail a trade-off between advantages and physiological costs in a sex-specific manner, exposing females to oxidative stress. This scenario may be aggravated during stressful periods, such as drought episodes when food is scarce, and it has implications for understanding female health, ageing and life span.