Competition for fertile females determines male reproductive success in many species. The priority of access model predicts that male dominance rank determines access to females, but this model has been difficult to test in wild populations, particularly in promiscuous mating systems. Tests of the model have produced variable results, probably because of the differing socioecological circumstances of individual species and populations. We tested the predictions of the priority of access model in the chimpanzees of Gombe National Park, Tanzania. Chimpanzees are an interesting species in which to test the model because of their fission-fusion grouping patterns, promiscuous mating system and alternative male mating strategies. We determined paternity for 34 offspring over a 22-year period and found that the priority of access model was generally predictive of male reproductive success. However, we found that younger males had higher success per male than older males, and low-ranking males sired more offspring than predicted. Low-ranking males sired offspring with younger, less desirable females and by engaging in consortships more often than high-ranking fathers. Although alpha males never sired offspring with related females, inbreeding avoidance of high-ranking male relatives did not completely explain the success of low-ranking males. While our work confirms that male rank typically predicts male chimpanzee reproductive success, other factors are also important; mate choice and alternative male strategies can give low-ranking males access to females more often than would be predicted by the model. Furthermore, the success of younger males suggests that they are more successful in sperm competition.