Competition over common-pool resources (CPR) is a ubiquitous challenge for social animals. Many species face similar dilemmas, yet our understanding of the evolutionary trajectory of CPR social strategies remains unexplored. Here, we provide a first look at the social strategies of our closest living relatives, chimpanzees (Pan troglodytes), in two novel resource dilemma experiments. Dyads of chimpanzees were presented with renewable resource systems, collapsible at a quantity-dependent threshold. Dyads had to continuously resist overconsumption to maximize collective gains. In study 1, dyads of chimpanzees sustained a renewing juice source. Inequality of juice acquisition between partners predicted sustaining success, indicating that one individual dominated the task while the partner inhibited. Dyads in study 2 fed together on accumulating carrot pieces but could end the accumulation any time by grabbing an immediate selfish source of carrots. Dyads with low tolerance were more successful at collectively sustaining the resource than highly tolerant dyads. Further, the dominant individual was more likely to cause collapse in dyads with low tolerance than dyads with high tolerance. These results indicate that chimpanzees use a dominance-based monopolisation strategy moderated by social tolerance to overcome the tragedy of the commons.