People frequently need to cooperate despite having strong self-serving motives. In the current study, pairs of 5- and 7-year-olds (N = 160) faced a one-shot coordination problem: To benefit, children had to choose the same of 3 reward divisions. They could not communicate or see each other and thus had to accurately predict each other's choices to succeed. One division split the rewards evenly, while the others each favored one child. Five-year-olds mostly chose the division favorable to themselves, resulting in coordination failure. By contrast, 7-year-olds mostly coordinated successfully by choosing the division that split the rewards equally (even though they behaved selfishly in a control condition in which they could choose independently). This suggests that by age 7, children jointly expect benefits to be shared among interdependent social partners "fairly" and that fair compromises can emanate from a cooperative rationality adapted for social coordination.