Living in large, stable social groups is often considered to favor the evolution of enhanced cognitive abilities, such as recognizing group members, tracking their social status and inferring relationships among them. An individual’s place in the social order can be learned through direct interactions with others, but conflicts can be time-consuming and even injurious. Because the number of possible pairwise interactions increases rapidly with group size, members of large social groups will benefit if they can make judgments about relationships on the basis of indirect evidence. Transitive reasoning should therefore be particularly important for social individuals, allowing assessment of relationships from observations of interactions among others. Although a variety of studies have suggested that transitive inference may be used in social settings, the phenomenon has not been demonstrated under controlled conditions in animals. Here we show that highly social pinyon jays (Gymnorhinus cyanocephalus) draw sophisticated inferences about their own dominance status relative to that of strangers that they have observed interacting with known individuals. These results directly demonstrate that animals use transitive inference in social settings and imply that such cognitive capabilities are widespread among social species.