That's absolutely possible.
From within the live chat, the day doesn't matter anyway. But it also works from the transcript.
Go to the transcript of the day with the first message, and select it for a conversation bookmark:
Then switch the to the day with the last message. It will remember the first message you selected on the previous page, and you can then choose the last message:
(ignore 3. on that screenshot, it's no longer necessary)
You can also switch the order around, selecting the last message first.
Finally, you can also select one of the two messages from the transcript and one from the live chat in the same manner.