Schizophrenia remains an evolutionary paradox. Its delusions, hallucinations and other symptoms begin in adolescence or early adulthood and so devastate sexual relationships and reproductive success that selection should have eliminated the disorder long ago. Yet it persists as a moderately heritable disorder at a global 1% prevalence--too high for new mutations at a few genetic loci. We suggest that schizophrenia persists and involves many loci because it is the unattractive, low-fitness extreme of a highly variable mental trait that evolved as a fitness ("good genes") indicator through mutual mate choice. Here we show that this hypothesis explains many key features of schizophrenia and predicts that some families carry modifier alleles that increase the indicator's neurodevelopmental sensitivity to heritable fitness and condition. Such alleles increase the extent to which high-fitness family members develop impressive courtship abilities and achieve high reproductive success, but also increase the extent to which low-fitness family members develop schizophrenia. Here we introduce this fitness indicator model of schizophrenia, discuss its explanatory power, explain how it resolves the evolutionary paradox, discuss its implications for gene hunting, and identify some empirically testable predictions as directions for further research.