Telomeric regions of the genome are inherently difficult-to-replicate due to their propensity to generate DNA secondary structures and form nucleoprotein complexes that can impede DNA replication fork progression. Precisely how cells respond to DNA replication stalling within a telomere remains poorly characterized, largely due to the methodological difficulties in analysing defined stalling events in molecular detail. Here, we utilized a site-specific DNA replication barrier mediated by the 'Tus/Ter' system to define the consequences of DNA replication perturbation within a single telomeric locus. Through molecular genetic analysis of this defined fork-stalling event, coupled with the use of a genome-wide genetic screen, we identified an important role for the SUMO-like domain protein, Esc2, in limiting genome rearrangements at a telomere. Moreover, we showed that these rearrangements are driven by the combined action of the Mph1 helicase and the homologous recombination machinery. Our findings demonstrate that chromosomal context influences cellular responses to a stalled replication fork and reveal protective factors that are required at telomeric loci to limit DNA replication stress-induced chromosomal instability.