Identifying mechanisms that underlie variation in adult survivorship provide insight into the evolution of life history strategies and phenotypic variation in longevity. There is accumulating evidence that shortening telomeres, the protective caps at the ends of chromosomes, play an important role in individual variation in longevity. Given that telomeres generally shorten with age, it was surprising to find that in a population of a long-lived seabird, Leach's storm petrel, telomeres appear to lengthen with age. This unique finding suggested that the longest lived individuals are able to elongate telomeres, an interpretation we call the “elongation hypothesis.” Alternatively, the “selection hypothesis” states that the longest lived individuals start with the longest telomeres and variation in telomere length decreases with age due to the selective disappearance of individuals with short telomeres. In the same population in which evidence supporting both hypotheses was uncovered, we tested mutually exclusive predictions from the elongation and selection hypotheses by measuring telomere length with the telomere restriction fragment assay in hatchling and old, adult storm petrels. As previously found, adult birds had longer telomeres on average compared with hatchlings. We also found that 3 hatchlings had mean telomere lengths exceeding that of the most extreme old bird, old birds on average had longer initial telomere lengths than hatchlings, and the variance in mean telomere length was significantly greater for hatchlings than for old birds, all predicted by the selection hypothesis. Perhaps more surprisingly, the oldest adults also show little or no accumulation of short telomeres over time, a pattern unknown in other species. Long telomeres are thought to provide a buffer against cellular senescence and be generally indicative of genome stability and overall cell health. In storm petrels, because the progressive accumulation of short telomeres appears negligible, variation in telomere length at birth may be linked to individual variation in longevity.