I highly recommend you just use
Google. Lots of information about finding a host or location to setup a free chat room for anything. Besides, everybody knows about social media as a communication tool (Skype, IRC, private group on Twitter and so on). Easy to research on Google.
These days people want mobility...being able to log into a chat via their mobile devices.
Yet, if you're worry about "not disturbing" someone's trading or your own trading...stay away from chat rooms.
Chat rooms
will be disturbing because you will need to "manage it" and "moderate" unless you're good at multi-tasking...trading and doing other online tasks. For example, coming to Elitetrader.com during the trading day to post messages...if you can do that during the trading session...chat rooms are about as easy to do like logging into ET forum to read/type messages during your trading day.
Yet, if you just want to chat with other NQ traders "after" the close...a lot tougher to start that type of chat room because now you're disturbing the free time or a time when many just want to call it a day and spend it with their family or friends.
If you're trading full time, profitable and tired of being alone at home while trading...you could setup
in person communication. A few traders meeting in person and trading together in the same room. I had something like that myself...in person meetings (an office) that we rented office space and setup our trading workstations in the office.
Advantages and disadvantages setting up an office for traders to communicate while trading.
When I stopped doing that...the group then moved to a private chat room because some of us moved to different states or different countries.
Stay away from "email chat rooms". You start a
chat room...you want it to be easy with
real-time messages. You want it timestamp, auto logs, history of the chats and mobile log in. You don't want to disturb people by asking them to open up their email to read messages...this isn't 1990.
Good luck...you should have one setup by end of day. It really is that easy.