That's a good idea.
It would help resolve non-sequiturs.
As a workround, I usually insert the move number into move-specific exchanges e.g. "good move #15".
Inserting a timestamp manually can be useful as a boundary marker, including identifying post-game remarks.
(Incidentally, this request Timestamp messages/moves in echess has been on the wishlists for at least 2 years - and resurfaced quite recently again).
I'm sure this subject would of been debated in the past.
What do people think of local timings on the last move and chat message board as an online settings selectable option. I would find this usefull when playing multiple opponent. So that I can easily work out the best time to play locally and international. ?