Rawls argued that fairness in human societies can be achieved if decisions about the distribution of societal rewards are made from behind a veil of ignorance, which obscures the personal gains that result. Whether ignorance promotes fairness in animal societies, that is, the distribution of resources to reduce inequality, is unknown. Here we show experimentally that cooperatively breeding banded mongooses, acting from behind a veil of ignorance over kinship, allocate postnatal care in a way that reduces inequality among offspring, in the manner predicted by a Rawlsian model of cooperation. In this society synchronized reproduction leaves adults in a group ignorant of the individual parentage of their communal young. We provisioned half of the mothers in each mongoose group during pregnancy, leaving the other half as matched controls, thus increasing inequality among mothers and increasing the amount of variation in offspring birth weight in communal litters. After birth, fed mothers provided extra care to the offspring of unfed mothers, not their own young, which levelled up initial size inequalities among the offspring and equalized their survival to adulthood. Our findings suggest that a classic idea of moral philosophy also applies to the evolution of cooperation in biological systems.