Sociality has evolved in many animal taxa, but primates are unusual because they establish highly differentiated bonds with other group members. Such bonds are particularly pronounced among females in species like baboons, with female philopatry and male dispersal. These relationships seem to confer a number of short-term benefits on females, and sociality enhances infant survival in some populations. However, the long-term consequences of social bonds among adult females have not been well established. Here we provide the first direct evidence that social relationships among female baboons convey fitness benefits. In a group of free-ranging baboons, Papio cynocephalus ursinus, the offspring of females who formed strong social bonds with other females lived significantly longer than the offspring of females who formed weaker social bonds. These survival benefits were independent of maternal dominance rank and number of kin and extended into offspring adulthood. In particular, females who formed stronger bonds with their mothers and adult daughters experienced higher offspring survival rates than females who formed weaker bonds. For females lacking mothers or adult daughters, offspring survival was closely linked to bonds between maternal sisters. These results parallel those from human studies, which show that greater social integration is generally associated with reduced mortality and better physical and mental health, particularly for women.