In-game chat has a nice feature of automagically inserted turn numbers before messages. It looks like

-------------Turn 1-----------------
2017/02/13 15:11:45 John Doe: good luck
2017/02/13 15:11:54 Jane Smith: have fun
-------------Turn 10---------------
2017/02/13 15:31:07 Jane Smith: good game
2017/02/13 15:31:18 John Doe: gg

This feature does not insert other important stages of the game: "before the game started", "territory distribution","after the game ended". It does not insert the turn number if all the messages were made on the same turn.
So if I say "hello" before the game and "good game" after the game, nothing is inserted.
Yes we have timestamps. But it is not easy to compare timestamps of turn 1 and timestamps of chat messages.

Fizzer's comment: I agree that would be a good feature. You should submit it to http://warlight.uservoice.com so it doesn't get lost.