"Εμείς μιλάμε στο chat."
Translation:We are talking on chat.
If you want to play by the book, foreign words are written in their own alphabet. Unless they've entered the Greek vocabulary which might be the case with "τσατ"
What you say "chat" which technology are you talking about? Text messaging? What's ap? Face time on an Apple? FB Messenger (text, audio, and/or video)?
The English expression sounds strange. Is it more common to say We are chatting on line?