You pretty much need an extension that runs in a separate window. You can already use Emacs through the Secure Shell[1] Chrome extension, but if you run it in a tab the browser eats too many key combinations for it to be useful. If you launch it in a separate window, then very few key combinations get intercepted and it works quite well.

[1] https://chrome.google.com/webstore/detail/secure-shell/iodih...