One of the challenges of cooperation is to coordinate with others. This is a challenge faced by both humans (Homo sapiens) and their closest living relatives, chimpanzees (Pan troglodytes). Both species coordinate their actions in a variety of contexts including group hunting, territory defence, and deciding direction of travel. However the cognitive mechanisms leading to successful coordination are not necessarily the same. Recently, theoretical accounts have proposed that humans have evolved unique skills for coordinating decisions and actions with others in the pursuit of common interests. We tested this hypothesis using a comparative approach by presenting pairs of 4 year old children and pairs of chimpanzees, our closest living relatives, with a very simple coordination problem. To succeed both individuals were required to choose the same one of four options. If successful they each received the same reward, so there were no conflicts of interest. Furthermore, the rewards associated with each option were identical, thus preferences for a particular option could not play a role. To investigate the flexibility of coordination we paired each individual with multiple partners. Our results showed that both species were able to achieve successful coordination, but there were marked differences in the way they did so. Children, using either communication or a leader-follower strategy, were able to coordinate quickly and flexibly, adjusting easily to new partners. In contrast, chimpanzees took time to converge on a single solution and started over from zero with each new partner, suggesting a lack of understanding of the process of coordination. Together, these results provide evidence for a divergence in the coordination skills of these two species and therefore the cognitive mechanisms underlying cooperation.