Encrypted Jabber
Jabber is this:


For technophobes, please go here: https://conversejs.org.

For people with privacy concerns, there's a new (2015) very excellent client for encrypted jabber, if you're using MacOS or Windows or Linux (or, I reckon, BSD): https://blog.torproject.org/blog/tor-messenger-beta-chat-over-tor-easily

Or you can use various other client apps (e.g. Adium or Pidgin), or you can use it via a web site (e.g. https://conversejs.org).

The only problem with jabber is that you need to set up a jabber account separately from setting up the client. There are lots of places you can get accounts: for example, https://www.calyxinstitute.org/projects/public_jabber_xmpp_server or https://conversejs.org.

BTW, although it's a hassle to have to set up a separate account, it's also a deliberate feature: it's so that people's information is decentralised, not all held by Google or Facebook or whoever.