You may want to view previous conversations in the Chat tool.  To do this, you can review the Session Logs of each chat session.

From the Course Home Page, click on Chat within the Communication dropdown menu.

chat menu

On the "Chat List" page, click on the dropdown associated with the chat you would like to review and select View Sessions. 

view sessions

On the "Chat Sessions" page, you will see all sessions from that chat room with the start and end date and time, duration, and messages sent for each session.  A chat session starts when someone enters the chat room and ends when the last person leaves the chat room.  To view a session log, click on the Start Date.

session date

When you are done reviewing the chat session, click the Done button at the bottom of the page. 

session details example