Telomeres, specialised structures that protect chromosome ends, play a critical role in preserving chromosome integrity. Telomere dynamics in the Tasmanian devil (Sarcophilus harrisii) are of particular interest in light of the emergence of devil facial tumour disease (DFTD), a transmissible malignancy that causes rapid mortality and threatens the species with extinction. We used fluorescent in situ hybridisation to investigate telomere length in DFTD cells, in healthy Tasmanian devils and in four closely related marsupial species. Here we report that animals in the Order Dasyuromorphia have chromosomes characterised by striking telomere length dimorphism between homologues. Findings in sex chromosomes suggest that telomere length dimorphism may be regulated by events in the parental germlines. Long telomeres on the Y chromosome imply that telomere lengthening occurs during spermatogenesis, whereas telomere diminution occurs during oogenesis. Although found in several somatic cell tissue types, telomere length dimorphism was not found in DFTD cancer cells, which are characterised by uniformly short telomeres. This is, to our knowledge, the first report of naturally occurring telomere length dimorphism in any species and suggests a novel strategy of telomere length control. Comparative studies in five distantly related marsupials and a monotreme indicate that telomere dimorphism evolved at least 50 million years ago.