Recently, Twitch implemented private group chats. Twitch viewers can finally discuss streams they're tuning into with friends without having to worry about the audience at large... provided they're members of the Twitch Partner Program.
Non-Twitch Partner Programs can still get a taste of what the sweet radio silence of a private Twitch group chat is like so long as they're invited into a private chat by a member. Members can create up to ten invite-only group chats and they'll have access to the same moderation tools in these private rooms as regular channel chat rooms.
For now, invite-only group chats will remain in beta "to make sure the new feature is stable and scalable." This feature is also only available on the web version of Twitch.
More information on the new feature can be found via the FAQ here.