In many diploid species, sex determination is linked to a pair of sex chromosomes that evolved from a pair of autosomes. In these organisms, the degeneration of the sex-limited Y or W chromosome causes a reduction in gene dose in the heterogametic sex for X- or Z-linked genes. Variations in gene dose are detrimental for large chromosomal regions when they span dosage-sensitive genes, and many organisms were thought to evolve complete mechanisms of dosage compensation to mitigate this. However, the recent realization that a wide variety of organisms lack complete mechanisms of sex chromosome dosage compensation has presented a perplexing question: How do organisms with incomplete dosage compensation avoid deleterious effects of gene dose differences between the sexes? Here we use expression data from the chicken (Gallus gallus) to show that ohnologs, duplicated genes known to be dosage-sensitive, are preferentially dosage-compensated on the chicken Z chromosome. Our results indicate that even in the absence of a complete and chromosome wide dosage compensation mechanism, dosage-sensitive genes are effectively dosage compensated on the Z chromosome.