Many of humans' most important social interactions rely on trust, including most notably among strangers. But little is known about the evolutionary roots of human trust. We presented chimpanzees (Pan troglodytes) with a modified version of the human trust game—trust in reciprocity—in which subjects could opt either to obtain a small but safe reward on their own or else to send a larger reward to a partner and trust her to reciprocate a part of the reward that she could not access herself. In a series of three studies, we found strong evidence that in interacting with a conspecific, chimpanzees show spontaneous trust in a novel context; flexibly adjust their level of trust to the trustworthiness of their partner and develop patterns of trusting reciprocity over time. At least in some contexts then, trust in reciprocity is not unique to humans, but rather has its evolutionary roots in the social interactions of humans' closest primate relatives.