Zymoseptoria tritici is a fungal pathogen of wheat. The genome of the reference isolate comprises 21 chromosomes of which eight are accessory. These chromosomes are not key determinants for virulence, as in other fungal pathogens, however, they are partly conserved among distinct Zymoseptoria species. Accessory chromosomes are highly instable during meiosis and mitosis, transcriptionally repressed and show enrichment of repetitive elements and heterochromatic histone marks. To elucidate if heterochromatic histone modifications have an impact on chromosome stability, we created deletion mutants of the methyltransferases responsible for H3K27me3 and H3K9me3. H3K27me3 is specifically associated with accessory chromosomes and subtelomeric regions in Z. tritici, while H3K9me3 is associated with repetitive elements. We combined experimental evolution, genetic and highresolution microscopic analyses to follow the impact of these deletions on chromosome and genome stability. We used ChIP-seq, genome sequencing and RNA-seq to compare changes in chromatin and genome structure and differences in gene expression between mutant and wild type strains. The loss of H3K9me3 results in dramatic chromatin reorganization, transposable element activation, genome rearrangements, formation of “neochromosomes” and increased accessory chromosome instability. Loss of H3K27me3, however, has little effect on chromatin organization and transposon control, but increases stability of the accessory chromosomes. We conclude that H3K9me3 strongly impacts chromatin and genome organization and that H3K27me3 has an important role in stability of accessory chromosomes. Epigenetic regulation is an important driver of genome evolution in this fungus and can contribute to rapid adaptation.