> Is there a service somewhere where you could simply send them a link, to open up a new tab in their browser, and commence a encrypted chat session right away ...
It might not actually exist in packaged form, but Secure Shell is everywhere now and it will do this easily, with an appropriate setup. Secure Shell relies on the same basic scheme as most modern encryption methods -- public-key cryptography.
With Secure Shell, one would have the normal peer-to-peer chat scheme, with one difference -- the communications channel would be encrypted using the SSH protocol, and both participants would have exchanged validations.
For a round-table chat with more than two participants, it becomes more complicated.
Wait, hold on -- I just thought of something simpler that does exist. You could use a Secure Sockets Layer approach. You would send your friend an URL preceded by "https://" and identifying a server that has a chat server and that supports the SSL protocol. That would be much simpler and it already exists. If you had a chat server running on an SSL server, each participant would be linked up securely, and the round table issue would be resolved.