To build such a website, you'd need a dedicated server hosting like Amazon
Web Services (
http://aws.amazon.com/) or a CouchDB hosting like IrisCouch (
http://www.iriscouch.com/service). In simpler terms: you can either rent a
server from someone (more expensive, but this will be your own server) or
try IrisCouch hosting, which is cheaper, easier to manage and good for a
start trials.
If you dont like Amazon, then rent a server from some other provider like
Rackspace (
http://www.rackspace.com/cloud/servers/)