Personalities are general properties of humans and other animals. Different personality traits are phenotypically correlated, and heritabilities of personality traits have been reported in humans and various animals. In great tits, consistent heritable differences have been found in relation to exploration, which is correlated with various other personality traits. In this paper, we investigate whether or not risk-taking behaviour is part of these avian personalities. We found that (i) risk-taking behaviour is repeatable and correlated with exploratory behaviour in wild-caught hand-reared birds, (ii) in a bi-directional selection experiment on 'fast' and 'slow' early exploratory behaviour, bird lines tend to differ in risk-taking behaviour, and (iii) within-nest variation of risk-taking behaviour is smaller than between-nest variation. To show that risk-taking behaviour has a genetic component in a natural bird population, we bred great tits in the laboratory and artificially selected 'high' and 'low' risk-taking behaviour for two generations. Here, we report a realized heritability of 19.3 +/- 3.3% (s.e.m.) for risk-taking behaviour. With these results we show in several ways that risk-taking behaviour is linked to exploratory behaviour, and we therefore have evidence for the existence of avian personalities. Moreover, we prove that there is heritable variation in more than one correlated personality trait in a natural population, which demonstrates the potential for correlated evolution.