Sexual selection theory predicts that because male reproductive success in mammals is limited by access to females, males will attempt to defend access to mates and exclude rivals from mating. In mammals, dominance rank is correlated with male reproductive success; however, the highest-ranking (alpha) male rarely monopolizes reproduction completely. To explain why, incomplete control models propose that alpha males simply cannot control other males' access to mates. If true, then dominance rank should be a key factor influencing subordinate (non-alpha) male mating success. Alternatively, the concession model states that alpha males can prevent other males from gaining access to mates but posits that they concede matings to subordinates in exchange for social favours. This predicts that a male's grooming interactions with the alpha should mediate his access to females. We test these predictions using 36 years of data, encompassing the tenures of eight alpha male chimpanzees at Gombe National Park, Tanzania. Incomplete control models were most strongly supported. At a given copulation event, the probability that the alpha was the male that mated was negatively associated with the number of males and sexually receptive females in the party. Additionally, as the number of males increased, high dominance rank was associated with an increased likelihood that a particular non-alpha male mated. The concession model, however, was also supported. The amount of time a male spent grooming with the alpha was positively associated with his likelihood of mating when the alpha was present in the party. As grooming is a major affiliative component of male social relationships, our results suggest that social bonds with dominant individuals are leveraged for mating access, particularly in species in which males form coalitions.