Chatroom for wordpress

HI Everyone!
I don’t know if this is the right place to put this or what. I am out of options, I have been searching for a couple days now with no luck.
I have a wordpress site that I want a chatroom on. The chatroom needs to be mobile compatible, so I guess that would mean HTML5. It doesn’t need to be anything fancy. I also would prefer it to be private so if it can install on my server that would be great. I am willing to pay, but not to much. If anybody knows of anything, it would be very much appreciated. Thanks!