In this paper, we study the effect on cesarean rates of a policy change in Chile that decreased the cost of delivery at private hospitals for women with public health insurance. Using a difference-in-differences (DID) approach based on the eligibility conditions for this benefit, we find that in the first three years after the policy took effect, deliveries in private hospitals increased by 8.7 percentage points, while the probability of a C-section being performed increased by 4.6 percentage points, with negative impacts on average newborn weight and size at birth. We show that the probability of an early term birth in hospitals participating in the program is an increasing function of expected hospital demand at the time of the full-term due date. This suggests that in the absence of price incentives, hospitals use C-sections to smooth out demand over time to optimize the use of their resources.