Abstract: A model for the evolution of cooperation shows that two conditions are necessary for cooperation to be stable: a hunting success rate that is low for single hunters and increases with group size, and a social mechanism limiting access to meat by non-hunters. Testing this model on TaI chimpanzees, Pan troglodytes, showed that (1) it pays for individuals to hunt in groups of three or four rather than alone or in pairs, and (2) cooperation is stable because hunters gain more at these group sizes than cheaters, owing to a meat-sharing pattern in which hunting, dominance and age, in that order, determine how much an individual gets. In addition, hunters provide cheaters (about 45% of the meat eaters) with the surplus they produce during the hunts. Thus, cooperation in Tai male chimpanzees is an evolutionarily stable strategy, and its success allows cheating to be an evolutionarily stable strategy for Tai female chimpanzees. In Gombe chimpanzees, cooperation is not stable, first, because hunting success is very high for single hunters, and second, because no social mechanism exists that limits access to meat by non-hunters. The analysis showed that some assumptions made when discussing cooperation in other social hunters might be wrong. This might downgrade our general perception of the importance of cooperation as an evolutionary cause of sociality.