There is now a significant and growing functional gap between the public Internet, whose basic architecture has remained unchanged for several decades, and a new generation of more sophisticated private networks. To address this increasing divergence of functionality and overcome the Internet's architectural stagnation, we argue for the creation of an Extensible Internet (EI) that supports in-network services that go beyond best-effort packet delivery. To gain experience with this approach, we hope to soon deploy both an experimental version (for researchers) and a prototype version (for early adopters) of EI. In the longer term, making the Internet extensible will require a community to initiate and oversee the effort; this paper is the first step in creating such a community.