Studies of genetic variation in metabolic traits have so far not focused on birds. In our study population of captive zebra finches we found evidence for a significant heritable genetic component in basal metabolic rate (BMR). Heritability of all morphological traits investigated (body mass, head length, tars length and wing length) was significantly larger than zero. All traits were positively phenotypically correlated. Eight of 10 genetic correlations presented in this study differed significantly from zero, all being positive, suggesting the possibility of correlated responses to any selection acting on the traits. When conditioned on the genetic variance in body mass, the heritability of BMR was reduced from 25% to 4%. Hence, our results indicate that genetic changes in BMR through directional selection are possible, but the potential for adaptation independent of body mass may be limited.