First reply, acknowledge
When to use: Use it as your opening reply the moment the customer arrives angry.
Response
customer name, I am really sorry -- specific issue is not okay, and I would be frustrated too. You are talking to a real person now, and I am going to help you get this sorted.
Here is what I am doing right now: immediate action. Give me about time estimate and I will come back with something concrete, not a brush-off.
If they stay heated
That is completely fair, and I am not going to argue with you. My job for the next few minutes is to fix this, so bear with me one moment while I pull up your account.
Why it works
It names the exact problem, drops the corporate shield, and commits to an immediate concrete action with a time -- which is what actually calms a live chat instead of a scripted sorry.