Unmanned Aerial Vehicles (UAVs), commonly referred to as drones, have recently seen an increased level of interest as their potential use in same-day home delivery has been promoted and advocated by large retailers and courier delivery companies. We introduce a novel way to exploit drones in same-day home delivery settings: drone resupply. We consider a home delivery system in which delivery vehicles are regularly resupplied by drones. Resupply can take place whenever a delivery vehicle is stationary and a drone can land on the vehicle's roof. We introduce the vehicle routing problem with drone resupply to capture and investigate this setting. We develop different algorithms and compare their performance. Finally, we quantify the potential benefits of drone resupply and generate valuable insights for advancing this concept.