Complete sex chromosome dosage compensation has more often been observed in XY than ZW species. In this study, using a population genetic model and the chicken transcriptome, we assess whether sexual conflict can account for this difference. Sexual conflict over expression is inevitable when mutation effects are correlated across the sexes, as compensatory mutations in the heterogametic sex lead to hyperexpression in the homogametic sex. Coupled with stronger selection and greater reproductive variance in males, this results in slower and less complete evolution of Z compared with X dosage compensation. Using expression variance as a measure of selection strength, we find that, as predicted by the model, dosage compensation in the chicken is most pronounced in genes that are under strong selection biased towards females. Our study explains the pattern of weak dosage compensation in ZW systems, and suggests that sexual selection plays a major role in shaping sex chromosome dosage compensation.