A novel approach to studying social relationships in captive adult chimpanzees (Pan troglodytes) was taken by using principal components analysis (PCA) to extract three key components of relationship quality from nine behavioural variables. Based on the loadings of the behavioural variables, the components appeared to match previously hypothesized critical aspects of social relationships and were therefore labelled Value, Compatibility and Security. The effects of kinship, sex combination, age difference and time spent together on each of the relationship quality components were analysed. As expected, kin were found to have more valuable, compatible and secure relationships than non-kin. Female–female dyads were found to be more compatible than male–male or mixed-sex dyads, whereas the latter were found to be most secure. Partners of a similar age were found to have more secure and more valuable relationships than those with a larger age gap. Individuals that were together in the group for longer were more valuable and more compatible, but their relationships were found to be less secure than individuals that were together in the group for a shorter time. Although some of the results may be unexpected based on chimpanzee socio-ecology, they fit well overall with the history and social dynamics of the study group. The methods used confer a significant advantage in producing quantitative composite measures of each component of relationship quality, obtained in an objective manner. These findings therefore promote the use of such measures in future studies requiring an assessment of the qualities of dyadic social relationships.