Zymoseptoria tritici is a plant pathogenic fungus specialized to infect wheat (Triticum aestivum). The genome of the sequenced reference isolate comprises 21 chromosomes of which eight are accessory chromosomes. These chromosomes are highly instable during meiosis and mitosis, transcriptionally repressed and show enrichment of repetitive elements and of heterochromatic histone marks. To elucidate the role of heterochromatin associated histone modifications on genome stability and transcriptional regulation in Z. tritici, we created deletion mutants of the methyltransferases KMT6 and KMT1 that are responsible for H3K27me3 and H3K9me3, respectively. We combined experimental evolution, genetics and high-resolution microscopic analyses to follow the impact of these deletions on chromosome and genome stability. Furthermore, we used ChIPseq, whole genome sequencing and RNAseq to compare changes in chromatin and genome structure and differences in gene expression between mutant and wild type strains. Analyses of genome and ChIPseq data from the Δkmt1 mutants reveal dramatic chromatin reorganization, genome rearrangements and formation of neochromosomes likely mediated by transposable element activation. The Δkmt6 mutant however displays an increased stability of the accessory chromosomes compared to the wild type under normal growth conditions in vitro. Based on these results we conclude a strong impact of H3K9me3 in chromatin and genome organization and an important role of H3K27me3 for the stability of accessory chromosomes.