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Telomere length predicts survival in birds, and many stressors that presumably reduce fitness have also been linked to telomere length. The response to selection of telomere length will be largely determined by the heritability of this trait; however, little is known about the genetic component of telomere length variation in animals other than humans. Moreover, published heritability estimates of telomere length are based on telomere measurements with techniques that do not distinguish between terminal telomeres, which are susceptible to age and stress, and the interstitial telomeric repeats, which are relatively inert. Heritability estimates that combine interstitial and terminal telomeres are difficult to interpret in species such as birds, where interstitial telomeres are often numerous. We estimated the heritability of terminal telomere length in a captive Zebra Finch population of cross-fostered (half-)siblings using data obtained with an electrophoresis technique that excludes the interstitial repeats from the measurements. We used both a Bayesian quantitative genetic 'animal' model and a frequentist sibling regression approach to estimate heritability. With the animal model, we estimated a high heritability of telomere length (h (2) = 0.99, 95 % credible interval = 0.87-1), but had insufficient statistical power to separate parental and permanent environment effects. The frequentist approach yielded similar heritability estimates, although with large confidence intervals. We used general linear mixed models to disentangle variance components of telomere length. The relative contributions of the individual, mother and father to telomere length variation were statistically indistinguishable at 23-31 %. Chicks were cross-fostered 4-days after hatching, and no effect of rearing nest was found, indicating that any undetected environmental effects exerted their influence prior to, or soon after, hatching. Thus, we conclude that telomere length resemblance between relatives is high and proportional to their relatedness, but we cannot conclusively distinguish between genetic and other forms of inheritance.