Language is a cognitively demanding human trait, but it is also a fundamentally cooperative enterprise that rests on the motivation to share information. Great apes possess many of the cognitive prerequisites for language, but largely lack the motivation to share information. Callitrichids (including marmosets and tamarins) are highly vocal monkeys that are more distantly related to humans than great apes are, but like humans, they are cooperative breeders and all group members help raising offspring. Among primates, this rearing system is correlated with proactive prosociality, which can be expressed as motivation to share information. We therefore propose that the unique coincidence of these two components in humans set the stage for language evolution: The cognitive component inherited from our great ape-like ancestors, and the motivational one added convergently as a result of cooperative breeding. We evaluate this scenario based on a review of callitrichd vocal communication and show that furthermore, they possess many of the mechanistic elements emphasized by the mirror system hypothesis of language evolution. We end by highlighting how more systematic phylogenetic comparisons will enable us to further promote our understanding of the role of cooperative breeding during language evolution.