Females of the arctiid moth Utetheisa ornatrix mate preferentially with larger males, receiving both direct phenotypic and indirect genetic benefits. Here we demonstrate that the female's mating preference is inherited through the father rather than the mother, indicating that the preference gene or genes lie mostly or exclusively on the Z sex chromosome, which is strictly paternally inherited by daughters. Furthermore, we show that the preferred male trait and the female preference for that trait are correlated, as females with larger fathers have a stronger preference for larger males. These findings are predicted by the protected invasion theory, which asserts that male homogametic sex chromosome systems (ZZ/ZW) found in lepidopterans and birds promote the evolution of exaggerated male traits through sexual selection. Specifically, the theory predicts that, because female preference alleles arising on the Z chromosome are transmitted to all sons that have the father's attractive trait rather than to only a fraction of the sons, such alleles will experience stronger positive selection and be less vulnerable to chance loss than would autosomal alleles.