•Nine-month-olds have expect a bystander to punish to unfair distributors and reward fair distributors.•These results reveal early-emerging expectations about punshments and rewards in third-party contexts.•These findings are consistent with the view that the principle of fairness is an evolved adaptation. Rewarding individuals who distribute resources fairly and punishing those who distribute resources unfairly may be very important actions for fostering cooperation. This study investigated whether 9-month-olds have some expectations concerning punishments and rewards that follow distributive actions. Infants were shown simple animations and were tested using the violation-of-expectation paradigm. In Experiment 1, we found that infants looked longer when they saw a bystander delivering a corporal punishment to a ‘fair distributor,' who distributed some windfall resources equally to the possible recipients, rather than to an ‘unfair distributor,' who distributed the resources unequally. This pattern of looking times was reversed when, in Experiment 2, punishments were replaced with rewards. These findings suggest an early emergence of expectations about punishing and rewarding actions in third-party contexts, and they help to evaluate competing claims about the origins of a sense of fairness.