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In social species, individuals may be able to overcome competitive constraints on cooperation by leveraging relationships with familiar, tolerant partners. While strong social ties have been linked to cooperation in several social mammals, it is unclear the extent to which weak social ties can support cooperation, particularly among non-kin. We tested the hypothesis that weakly affiliative social relationships support cooperative coalition formation using 10 years of behavioural data on wild female chimpanzees. Female chimpanzees typically disperse and reside with non-kin as adults. Their social relationships are differentiated but often relatively weak, with few dyads sharing strong bonds. Females occasionally form aggressive coalitions together. Three measures of relationship quality—party association, five-metre proximity and whether a dyad groomed—positively predicted coalitions, indicating that relationship quality influenced coalition partnerships. However, dyads that groomed frequently did not form more coalitions than dyads that groomed occasionally, and kin did not cooperate more than expected given their relationship quality. Thus, strong bonds and kinship did not bolster cooperation. We conclude that cooperative coalitions among female chimpanzees depend on social tolerance but do not require strong bonds. Our findings highlight social tolerance as a distinct pathway through which females can cultivate cooperative relationships. This article is part of the theme issue ‘Cooperation among women: evolutionary and cross-cultural perspectives’.