Chimpanzees (Pan troglodytes) frequently participate in social exchange involving multiple goods and services of variable value, yet they have not been tested in a formalized situation to see whether they can barter using multiple tokens and rewards. We set up a simple barter economy with two tokens and two associated rewards and tested chimpanzees on their ability to obtain rewards by returning the matching token in situations in which their access to tokens was unlimited or limited. Chimpanzees easily learned to associate value with the tokens, as expected, and did barter, but followed a simple strategy of favoring the higher-value token, regardless of the reward proffered, instead of a more complex but more effective strategy of returning the token that matched the reward. This response is similar to that shown by capuchin monkeys in our previous study. We speculate that this response, while not ideal, may be sufficient to allow for stability of the social exchange system in these primates, and that the importance of social barter to both species may have led to this convergence of strategies.