Checkpoint mechanisms that respond to DNA damage in the mitotic cell cycle are necessary to maintain the fidelity of chromosome transmission. These mechanisms must be able to distinguish the normal telomeres of linear chromosomes from double-strand break damage. However, on several occasions, Drosophila chromosomes that lack their normal telomeric DNA have been recovered, raising the issue of whether Drosophila is able to distinguish telomeric termini from nontelomeric breaks. We used site-specific recombination on a dispensable chromosome to induce the formation of a dicentric chromosome and an acentric, telomere-bearing, chromosome fragment in somatic cells of Drosophila melanogaster. The acentric fragment is lost when cells divide and the dicentric breaks, transmitting a chromosome that has lost a telomere to each daughter cell. In the eye imaginal disc, cells with a newly broken chromosome initially experience mitotic arrest and then undergo apoptosis when cells are induced to divide as the eye differentiates. Therefore, Drosophila cells can detect and respond to a single broken chromosome. It follows that transmissible chromosomes lacking normal telomeric DNA nonetheless must possess functional telomeres. We conclude that Drosophila telomeres can be established and maintained by a mechanism that does not rely on the terminal DNA sequence.