The chromatin landscape is key for gene regulation, but little is known about how it differs between sexes or between species. Here, we study the sex-specific chromatin landscape of Drosophila miranda, a species with young sex chromosomes, and compare it with Drosophila melanogaster. We analyze six histone modifications in male and female larvae of D. miranda (H3K4me1, H3K4me3, H3K36me3, H4K16ac, H3K27me3, and H3K9me2), and define seven biologically meaningful chromatin states that show different enrichments for transcribed and silent genes, repetitive elements, housekeeping, and tissue-specific genes. The genome-wide distribution of both active and repressive chromatin states differs between males and females. In males, active chromatin is enriched on the X, relative to females, due to dosage compensation of the hemizygous X. Furthermore, a smaller fraction of the euchromatic portion of the genome is in a repressive chromatin state in males relative to females. However, sex-specific chromatin states appear not to explain sex-biased expression of genes. Overall, conservation of chromatin states between male and female D. miranda is comparable to conservation between D. miranda and D. melanogaster, which diverged >30 MY ago. Active chromatin states are more highly conserved across species, while heterochromatin shows very low levels of conservation. Divergence in chromatin profiles contributes to expression divergence between species, with~26% of genes in different chromatin states in the two species showing species-specific or species-biased expression, an enrichment of approximately threefold over null expectation. Our data suggest that heteromorphic sex chromosomes in males (that is, a hypertranscribed X and an inactivated Y) may contribute to global redistribution of active and repressive chromatin marks between chromosomes and sexes.