Many users face surveillance of their Internet communications and a significant fraction suffer from outright blocking of certain destinations. Anonymous communication systems allow users to conceal the destinations they communicate with, but do not hide the fact that the users are using them. The mere use of such systems may invite suspicion, or access to them may be blocked. We therefore propose Cirripede, a system that can be used for unobservable communication with Internet destinations. Cirripede is designed to be deployed by ISPs; it intercepts connections from clients to innocent-looking destinations and redirects them to the true destination requested by the client. The communication is encoded in a way that is indistinguishable from normal communications to anyone without the master secret key, while public-key cryptography is used to eliminate the need for any secret information that must be shared with Cirripede users. Cirripede is designed to work scalably with routers that handle large volumes of traffic while imposing minimal overhead on ISPs and not disrupting existing traffic. This allows Cirripede proxies to be strategically deployed at central locations, making access to Cirripede very difficult to block. We built a proof-of-concept implementation of Cirripede and performed a testbed evaluation of its performance properties.