Eonet comes with an embeded 1-to-1 live chat. Every logged in member will be able to chat with another one using the chat bar on the right:
You can edit many settings of the chat in Theme Settings > Community > Chat.
The chat get automatically the most recent conversation between users, if there isn’t any conversation within users, then it will create a new one with the subject “Chat conversation”.
The theme also show live informatiosn on members in the bar, such as “user onlin” or “new message received”. These informations are loaded every 20 seconds and they don’t need that the page is refreshed to be displayed.