Can improved last-mile logistics change where women give birth? This question is particularly important in settings where unreliable medical supply chains can limit the quality and availability of care even when health facilities are physically accessible. This paper studies a medical drone delivery network that supplied blood products and other urgent medical supplies to health facilities. I exploit the rollout of the network and link district-level drone exposure to birth histories from the Rwanda Demographic and Health Surveys (DHS). The main analysis focuses on districts treated by the first drone hub in 2017. Using a difference-in-differences design, I find that drone exposure increased hospital delivery by 2.6 percentage points. Adding districts treated in 2019 yields a similar 3.0 percentage-point increase, suggesting that the choice of treatment cohort does not drive the result. I also find evidence of declines in infant mortality following drone exposure, consistent with improved hospital capacity to respond to complications. Together, these findings suggest that improving the reliability of medical supply chains can influence healthcare-seeking behavior and improve maternal and infant health. More broadly, the findings show how medical drones can enable healthcare technology leapfrogging by overcoming logistical constraints, making health facilities more reliable, and encouraging women to seek facility-based care.