Evolution is driven by the accumulation of competing mutations that influence survival. A broad form of genetic variation is the amplification or deletion of DNA (≥50 bp) referred to as copy number variation (CNV). In humans, CNV may be inconsequential, contribute to minor phenotypic differences, or cause conditions such as birth defects, neurodevelopmental disorders, and cancers. To identify mechanisms that drive CNV, we monitored the experimental evolution of Saccharomyces cerevisiae populations grown under sulfate-limiting conditions. Cells with increased copy number of the gene SUL1, which encodes a primary sulfate transporter, exhibit a fitness advantage. Previously, we reported interstitial inverted triplications of SUL1 as the dominant rearrangement in a haploid population. Here, in a diploid population, we find instead that small linear fragments containing SUL1 form and are sustained over several generations. Many of the linear fragments are stabilized by de novo telomere addition within a telomere-like sequence near SUL1 (within the SNF5 gene). Using an assay that monitors telomerase action following an induced chromosome break, we show that this region acts as a hotspot of de novo telomere addition and that required sequences map to a region of <250 base pairs. Consistent with previous work showing that association of the telomere-binding protein Cdc13 with internal sequences stimulates telomerase recruitment, mutation of a four-nucleotide motif predicted to associate with Cdc13 abolishes de novo telomere addition. Our study suggests that internal telomere-like sequences that stimulate de novo telomere addition can contribute to adaptation by promoting genomic plasticity.