Socioecological environments that promote frequent interaction and social tolerance have favored the evolution of strong and equitable social bonds, which facilitate cooperation and confer fitness benefits. In most species, kinship is the primary predictor of bond strength and quality, but it does not adequately explain partner choice among adult male chimpanzees. Instead, most bonds and cooperative interactions occur among unrelated individuals, likely because of a lack of brothers among available partners. To identify what factors drive partner choice when kinship does not, we investigated the strength and quality of social bonds among adult male chimpanzees (N = 26) at Gombe National Park, Tanzania. Maternal brothers, when present, formed stronger bonds than other dyads, and maternal brothers who were close in age or rank formed the strongest bonds. Among dyads that were not maternal brothers, however, the strength of social bonds was not associated with either age difference or rank difference. Additionally, dyads with stronger bonds groomed more equitably than other dyads, as did maternal brothers and dyads close in rank. Bonds were stable, community-wide, for 2 years on average, while lasting up to 13 years. Overall, there remains no clear-cut explanation for partner choice among male chimpanzees. Demographic constraints limit the impact of kinship, and the effects of age and rank difference are small or nonexistent, suggesting that bond strength results from a more complex process than a simple accounting of basic characteristics. Instead, dyads may possess some distinct quality that engenders strength and stability, such as compatible personalities. Strong social ties are associated with increased fitness in several species, including humans, baboons, feral horses, and dolphins. Although close kin typically form the strongest bonds, kinship explains only a limited number of bonds (and associated cooperation) among adult male chimpanzees. To identify what factors influence partner choice when kinship does not, we examined social bonds among adult male chimpanzees at Gombe National Park, Tanzania. Males formed strong, stable bonds and groomed more equitably with strong bond partners. Nevertheless, kinship, age difference, and rank difference did not fully explain male partner choice. These results contrast with findings in other species, where stronger and more equitable bonds are typically formed by kin as well as those that are close in age and rank. Instead, male chimpanzee dyads may possess some distinct quality that promotes strength and stability, such as compatible personalities.