The cooperative abilities of captive chimpanzees, Pan troglodytes, in experiments do not match the sophistication that might be predicted based on their naturally occurring cooperative behaviours. This discrepancy might partly be because in previous experiments potential chimpanzee cooperators were partnered without regard to their social relationship. We investigated the ability of chimpanzee dyads to solve a physical task cooperatively in relation to their interindividual tolerance levels. Pairs that were most capable of sharing food outside the test were also able to cooperate spontaneously (by simultaneously pulling two ropes) to obtain food. In contrast, pairs that were less inclined to share food outside of the test were unlikely to cooperate. Furthermore, previously successful subjects stopped cooperating when paired with a less tolerant partner, even when the food rewards were presented in a dispersed and divisible form to reduce competition between subjects. These results show that although chimpanzees are capable of spontaneous cooperation in a novel instrumental task, tolerance acts as a constraint on their ability to solve such cooperative problems. This finding highlights the importance of controlling such social constraints in future experiments on chimpanzee cooperation, and suggests that the evolution of human-like cooperative skills might have been preceded by the evolution of a more egalitarian social system and a more human-like temperament.