Telomeres are protective caps at the end of eukaryotic chromosomes that shorten with age and in response to stressful or resource-demanding conditions. Their length predicts individual health and lifespan across a wide range of animals, but whether the observed positive association between telomere length and lifespan is environmentally induced, or set at conception due to a shared genetic basis, has not been tested in wild animals. We applied quantitative genetic "animal models" to longitudinal telomere measurements collected over a 10-year period from individuals of a wild seabird (common tern; Sterna hirundo) with known pedigree. We found no variation in telomere shortening with age among individuals at the phenotypic and genetic level, and only a small permanent environmental effect on adult telomere length. Instead, we found telomere length to be highly heritable and strongly positively genetically correlated with lifespan. Such heritable differences between individuals that are set at conception may present a hitherto underappreciated component of variation in somatic state.