The integrity of the genome relies on the maintenance of chromosomes, the structural embodiment of the genetic material. Disruption of chromosome replication can lead to extensive genomic rearrangements, spanning kilobase (Kb) to megabase (Mb) regions. Some chromosome rearrangements are inherently dynamic, beginning as a single unstable rearrangement from which multiple rearrangements emerge. The rare formation and transient behavior of unstable chromosomes renders their study challenging. Here I characterize the genetic ontogeny of unstable chromosomes in a budding yeast model, from initial replication error to unstable chromosome formation to their resolution. I find that the initial error often arises in or near the telomere and frequently forms unstable chromosomes that later resolve to an internal "collection site" in the middle of the chromosome. The initial telomere-proximal unstable chromosome is increased in cells mutant for telomerase, the Tel1 checkpoint kinase and even the Rad9 checkpoint protein, with no known telomere-specific function. Defects in Tel1 and the Rrm3 DNA helicase, or the Tel1-MRX complex and 9-1-1 checkpoint clamp, synergize dramatically to generate unstable chromosomes, further illustrating the consequence of replication error in the telomere. I performed a candidate genetic screen of instability in telomere maintenance and DNA damage response (DDR) proteins to characterize the interplay of pathways regulating senescence and genomic instability. Collectively, my results suggest that unstable chromosomes form in or near damaged telomeres, independently of end degradation (Exo1-independent), by either nonhomologous end joining (partially Lig4-dependent) or by faulty template switch during replication (Lig4- and Rad52-independent). The telomere-proximal unstable chromosomes then rearrange further to the middle of the chromosome. These results implicate telomere replication errors as a common source of widespread genomic changes and make substantial progress to our understanding of the initiation and fate of unstable chromosomes in the eukaryotic genome.