Yeast strains were constructed in which a single telomere could be eliminated from the end of a dispensable chromosome. In wild-type cells, elimination of a telomere caused a RAD9-mediated cell cycle arrest, indicating that telomeres help cells to distinguish intact chromosomes from damaged DNA. However, many cells recovered from the arrest without repairing the damaged chromosome, replicating and segregating it for as many as ten cell divisions prior to its eventual loss. Telomere elimination caused a dramatic increase in loss of the chromosome in all strains examined, demonstrating that yeast telomeres are also essential for maintaining chromosome stability. Thus, in spite of checkpoint and DNA damage repair systems, many chromosomes that lose a telomere are themselves destined for loss.