Can one chat extend to all of my site?

I have a multi site, let’s call it site A, B & C and I have network activated the chat plug in.

I go site A and start a chat with another user, however the chat is lost if I move on to site B or C, the chat does not return till I go back to site A.

My question is this. Is it possible to start a chat in Site A and continue it through any part of my site as I or any of my users move around. Maybe I have configured it wrong and if so I apologise.

Apart from that I love it!