Animals of many species show consistency in behaviour across time and contexts that differs from other individuals' behaviour in the same population. Such ‘personality’ affects fitness and has therefore become an increasingly relevant research topic in biology. However, consistent variation in social behaviour is understudied. In socially living species, behaviour occurs in a social environment and social interactions have a significant influence on individual fitness. This study addressed personality in social behaviour of 75 captive chimpanzees in three zoos by coding observed behaviour. Fifteen behavioural variables were significantly repeatable (range 0.21–0.93) in at least two of the three zoos. The behaviours showed considerable long-term stability across 3 years, which did not differ from the short-term repeatability. The repeatable behaviours were then analysed with factor analyses. They formed five independent factors, three of which consisted of social traits and were labelled ‘sociability’, ‘positive affect’ and ‘equitability’. The two non-social behaviour factors were labelled ‘anxiety’ and ‘activity’. The factor scores were analysed for sex and population differences. Males had higher factor scores in all traits except ‘sociability’. The factor scores differed also between the zoos, implying considerable external effects in trait expression. The results show that chimpanzees show personality in a broad range of social and non-social behaviours. The study highlights the importance of assessing personality in the social behaviour, especially in cohesive social species, as only then can we understand the consequences of personality in socially living species.