It has become increasingly important for content providers (CPs) to reach consumers with low latency. Peering links that connect CPs directly to access Internet service providers (access ISPs) have been used for this purpose thus providing one-hop AS paths from CPs to users. While providing improved latency, these peering links still do not give CPs control over the entire end-to-end path to their users. This has made it difficult for CPs to completely manage user experience. Motivated by this, we propose the deployment of Zero-Hop Networks (ZeN), where a CP's entire end-to-end path to users is under its control. We believe it is important to respond to the compelling demand for ZeN and enable its provision over the shared Internet infrastructure so that all may continue to reap its benefits. In this paper we lay out the vision for ZeN, describing its goals and challenges. We propose to deploy ZeN by allowing CPs to extend their network's control over the access ISP substrate in a way that allows the CP to control the entire end-to-end path. We develop two strawman architectures based on Software-Defined Networking ideas: one based on resource reservation and the other based on network virtualization. We also discuss some elements of a research agenda that is needed to bring ZeN deployments to realization.