We discussed this internally the other week and we agree that this would be handy to have. Especially in cases where a moderator pings several community team members at a time and one of us responds before the others.
Using our existing chat UI and some inspiration from how Twitter shows linked tweets, we would like to propose the following implementation.
This conversation view will be accessible from the pop-up you get when clicking on the arrow to the left of every message:
Clicking "view conversation" would go to a view similar to the existing chat transcripts. It will show the current message, the message it is in reply to (and the ones before it), as well as the messages that were posted in reply to it. Plus a message or two around each of those, just to account for people like me who are fond of posting a linked @reply, followed immediately by another related message that's not linked to anything else.
Other messages that appear in the transcript can be hidden and indicated the same way the Highlights view shows skipped posts:
Ideally, clicking that would expand the transcript and show the messages that were hidden, but that's optional. Using one of the displayed messages to get to the full transcript would be easy/good enough.