What is morality? And to what extent does it vary around the world? The theory of “morality-as-cooperation” argues that morality consists of a collection of biological and cultural solutions to the problems of cooperation recurrent in human social life. Morality-as-cooperation draws on the theory of non-zero-sum games to identify distinct problems of cooperation and their solutions, and it predicts that specific forms of cooperative behavior—including helping kin, helping your group, reciprocating, being brave, deferring to superiors, dividing disputed resources, and respecting prior possession—will be considered morally good wherever they arise, in all cultures. To test these predictions, we investigate the moral valence of these seven cooperative behaviors in the ethnographic records of 60 societies. We find that the moral valence of these behaviors is uniformly positive, and the majority of these cooperative morals are observed in the majority of cultures, with equal frequency across all regions of the world. We conclude that these seven cooperative behaviors are plausible candidates for universal moral rules, and that morality-as-cooperation could provide the unified theory of morality that anthropology has hitherto lacked.