The advances in unmanned aerial vehicle (UAV) technology have empowered mobile operators to deploy LTE base stations (BSs) on UAVs, and provide on-demand, adaptive connectivity to hotspot venues as well as emergency scenarios. However, today’s evolved packet core (EPC) that orchestrates the LTE RAN faces fundamental limitations in catering to such a challenging, wireless and mobile UAV environment, particularly in the presence of multiple BSs (UAVs). In this work, we argue for and propose an alternate, radical edge EPC design, called SkyCore that pushes the EPC functionality to the extreme edge of the core network – collapses the EPC into a single, light-weight, self-contained entity that is co-located with each of the UAV BS. SkyCore incorporates elements that are designed to address the unique challenges facing such a distributed design in the UAV environment, namely the resource-constraints of UAV platforms, and the distributed management of pronounced UAV and UE mobility. We build and deploy a fully functional version of SkyCore on a two-UAV LTE network and showcase its (i) ability to interoperate with commercial LTE BSs as well as smartphones, (ii) support for both hotspot and standalone multi-UAV deployments, and (iii) superior control and data plane performance compared to other EPC variants in this environment.