We examine how the effects of incentivizing individuals to use healthcare depend on the capacity of the health system. We study a conditional cash transfer program (JSY) in India that paid women to give birth in medical facilities. We find that JSY doubled the number of deliveries for which the average facility was responsible. In areas with below-median capacity, JSY increased perinatal mortality. Adverse effects spilled over onto rates of childhood vaccinations suggesting a diversion of resources from routine services. Our results indicate that health-system capacity is of first-order importance in determining whether demand-side policies are beneficial or harmful.