We propose a new model for the association of chromatin state and sex-bias in expression. We hypothesize enrichment of open chromatin in the sex where we see expression bias (OS) and closed chromatin in the opposite sex (CO). In this study of D. melanogaster and D. simulans head tissue, sex-bias in expression is associated with H3K4me3 (open mark) in males for male-biased genes and in females for female-biased genes in both species. Sex-bias in expression is also largely conserved in direction and magnitude between the two species on the X and autosomes. In male-biased orthologs, the sex-bias ratio is more divergent between species if both species have H3K27me2me3 marks in females compared to when either or neither species has H3K27me2me3 in females. H3K27me2me3 marks in females are associated with male-bias in expression on the autosomes in both species, but on the X only in D. melanogaster . In female-biased orthologs the relationship between the species for the sex-bias ratio is similar regardless of the H3K27me2me3 marks in males. Female-biased orthologs are more similar in the ratio of sex-bias than male-biased orthologs and there is an excess of male-bias in expression in orthologs that gain/lose sex-bias. There is an excess of male-bias in sex-limited expression in both species suggesting excess male-bias is due to rapid evolution between the species. The X chromosome has an enrichment in male-limited H3K4me3 in both species and an enrichment of sex-bias in expression compared to the autosomes.