Competition among mammalian carnivores can be particularly intense and can influence population dynamics at lower trophic levels. One strategy employed by carnivores to minimize potentially costly interspecific competition is avoidance of dominant species. Recent research has highlighted the importance of consistent individual differences in behavior (i.e. temperament traits) in understanding behavioral variation during predator–prey interactions and intraspecific interactions. However, the importance of such individual differences to interspecific competition has received little attention. Here, we examined the responses of spotted hyenas (Crocuta crocuta) to their primary competitors, African lions (Panthera leo), to (1) determine whether hyenas avoid lions and (2) evaluate the potential importance of individual differences in behavior during interspecific competition. Spotted hyenas and lions co-occur throughout much of Africa and are vigorous competitors. Whereas lions sometimes kill hyenas and steal their food, lions also represent a source of food for hyenas via scavenging. Using audio playback experiments, we found that hyenas do not uniformly avoid potential encounters with lions. Indeed, we noted considerable variation among individuals in their responses to lion roars, and this variation reflected consistent individual differences in risk-taking and vigilance tendencies. Individual differences in vigilance behavior were specific to interactions with lions. We conclude that individual differences in behavior have the potential to play an important role in determining the nature and outcome of interspecific competition.