Blog owner and visitors messaging/chatting on mobiles

Hello guys,

I´d like to have the possibilty to make users able to visit my blog on their mobiles and integrate a good chat function, so I can chat with them like in a messaging app. But without having to make them log in and see other stuff in the backend. Even the admin bar is too much. Just the chat (with saved chat log) is needed.

How can I acchieve that?