Long-term collaborative relationships require that any jointly produced resources be shared in mutually satisfactory ways. Prototypically, this sharing involves partners dividing up simultaneously available resources, but sometimes the collaboration makes a resource available to only one individual, and any sharing of resources must take place across repeated instances over time. Here, we show that beginning at 5 years of age, human children stabilize cooperation in such cases by taking turns across instances of obtaining a resource. In contrast, chimpanzees do not take turns in this way, and so their collaboration tends to disintegrate over time. Alternating turns in obtaining a collaboratively produced resource does not necessarily require a prosocial concern for the other, but rather requires only a strategic judgment that partners need incentives to continue collaborating. These results suggest that human beings are adapted for thinking strategically in ways that sustain long-term cooperative relationships and that are absent in their nearest primate relatives.