Cooperative care and defense of young are hypothesized to be foundational to the societies of several species, including the sperm whale (Physeter macrocephalus). However, the extent of allocare among sperm whales and the mechanisms driving it have not been well-characterized. Sperm whale social units are matrilineally-based, making kin selection a likely key driver of allocare, but the relationship between kinship and calf care is essentially unknown. We investigate calf care in the context of kinship, by combining association and interaction data with genetic profiles for 16 calves from 7 eastern Caribbean social units. Mothers were the primary associate for 62.5% of calves, and the primary nurse for 87.5%, so behavioral observations are not always sufficient for assigning maternity. Babysitting and allonursing were frequent in some cases, particularly for calves less than a year old. Within social units, babysitting rates were correlated with relatedness (rs = 0.4, p < 0.05), and allonurses were, on average, closer maternal relatives of the calves they nursed than were available females who were not allonurses (Δr = 0.14, p = 0.054). Exceptions to the overall positive relationship between allocare and kinship suggest that additional factors influencing allocare among sperm whales may include reciprocity, group augmentation and gaining maternal experience.