Discord isn't just a voice-chat service for young gamers, it hosts text-chat too and is like IRC for a modern generation. Except everything is stored on their servers and you can scroll back through a channel's chat history to its beginning.
It's free to create your channel, then you can create multiple rooms, set permissions for individual members and their levels of access. Probably the easiest solution right now for text roleplay.
There are groups within Discord acting as a hub for RP Groups, but when I browsed it there wasn't anything I'd consider "serious roleplay". Some groups like this one appeared better organised.http://www.encounterroleplay.com/play-w ... tavern-rp/
The service itself can be accessed from here, without needing to install the app/client:https://discordapp.com/