Social dominance influences many aspects of the life of animals living in social groups, including fitness. Recent work suggests that individuals occupying different positions in a dominance hierarchy may differ in their behavioural and cognitive traits. The first objective of this thesis was to determine whether personality (i.e. consistent behavioural differences between individuals) is correlated with dominance in natural groups of black-capped chickadees (Poecile atricapillus) in the wild. Dominance relationships within these groups were highly asymmetrical and transitive, which is typical of linear dominance hierarchies. None of the measured personality traits (i.e. aggressiveness in hand, exploration, activity and neophilia) were significantly correlated with dominance. These results suggest that personality does not contribute to the formation of black-capped chickadee hierarchies and add to the growing body of evidence that inherent attributes of individuals are not sufficient to explain the structure of linear dominance hierarchies observed in the wild. The second objective of this thesis was to investigate how dominance and correlates of competitive ability (i.e. sex, age and body condition) are related to novel problem-solving performance, which is a proxy for innovativeness, the invention of new behavioural patterns or the modification of an existing behaviour in a novel context. Problem-solving performance was not significantly associated with sex, age or body condition, but dominants were more efficient problem-solvers than subordinates. This finding suggests that efficiency when solving a novel problem might be driven by cognitive capacity instead of the necessity induced by the social position of an individual. Overall, results of this thesis help to better understand dominance hierarchies in wild groups of animals.