Can improved last-mile logistics change where women give birth? This is an important question 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 phased rollout of the network and link district-level drone exposure to birth histories from the Rwanda Demographic and Health Surveys (DHS) 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 drone exposure reduced infant mortality following drone exposure, consistent with improved hospital capacity to respond to complications. Together, these findings show that improving last-mile medical logistics can affect both the capacity of health facilities and healthcare-seeking behavior. More broadly, the results illustrate how technologies that overcome infrastructure and supply-chain constraints can facilitate leapfrogging in low-resource settings.