Factors governing the faithful replication of chromosomes are essential for cellular and genomic integrity. While a variety of mechanisms to manage breaks and promote repair of DNA are widely recognized, epigenetic landmarks that preserve telomere-to-telomere replication fidelity and prevent genome instability are not well-understood. SETD2 is the histone methyltransferase responsible for trimethylation on histone H3 lysine 36 and is newly recognized as a tumor suppressor that acts to maintain genome stability. Importantly, SETD2 is frequently lost in cancers that exhibit extensive intratumoral heterogeneity. Here, we demonstrate that loss of SETD2 and H3K36me3 promotes chromosome segregation errors and DNA bridging during mitosis, and that these bridges are driven by the formation of dicentric chromosomes. Cytogenetic analyses revealed that these chromosomes were comprised of mirror-imaged isochromosomes and isodicentric chromosomes that contain two active centromeres. These data demonstrate that the SETD2 histone methyltransferase is essential to prevent a palindromic replication intermediate, whose loss precipitates the formation of a mutable chromatin structure known to initiate a cascade of genomic instability in cancer.