Cool project. I'm curious why you don't use Tor to provide peer-to-peer connectivity? It gives you NAT hole-punching and encryption for free. It seems the obvious choice.
Thanks for checking out the project! Chitchatter uses https://github.com/dmotz/trystero for peer connectivity, which doesn't support Tor. I don't know how Tor would be supported in a typical web browser. Have you seen Tor being used directly in that way?
For an alternative (but sadly barely-used) chat protocol that does use Tor, see Ricochet: https://en.wikipedia.org/wiki/Ricochet_(software)