A complex dynamic of social interactions can be created when individuals are confronted with conspecifics. When animals defend aggressively a spatial area and resources from intruders, the aggressiveness of the opponents is supposedly mainly related to the location where the agonistic interactions occur. The growing interest in consistent individual differences in behaviour (i.e. personality) could, however, improve our understanding of aggression and dominance, as it suggests the existence of individual variation in aggressive tendencies. Using only the proximity of individuals to their territory to explain their propensity to win a contest could therefore not be sufficient to entirely explain the outcome of these agonistic events. We investigated these questions in the eastern chipmunk (Tamias striatus), a small, and solitary, central-place foraging Sciurid that actively competes for patchy resources, and aggressively defends the area around its burrow. We recorded multiple agonistic interactions among marked individuals that competed for food resources experimentally supplied at different distances from their burrows. Using a mixed-model approach, where both individuals were considered either as focal or as opponent during a given agonistic encounter, we estimated the effect of individual variation in aggressiveness or in the tendency to trigger aggression. Although the outcome of the contests was classically linked to the proximity of each individual's burrow, a great part of the variation was captured by the identity of the two interacting individuals. Individuals differed significantly in their tendency to overthrow their adversaries, thus showing consistent aggressiveness. Furthermore, we found individual differences in reaction norms of aggressiveness as a response to proximity to the burrow. Considering individual variation might therefore bring new insights to fully understand social aggressive interactions, especially for territorial species. Measures of intrinsic individual aggressiveness corrected by the social context can also be used in a behavioral syndrome approach to investigate how they can be linked to other personality traits.