As noted above, when users click on the Chat button from a classroom's Main Menu, they are presented with a Chat Transcripts page:

The transcripts are a complete listing of every message typed by users while they were in that classroom's channel. As shown above, the transcripts are organized by day. Next to each day is the number of messages typed that day.
Click on the "Read" hyperlink to view the transcripts for a particular day:

The messages typed in the Chat on that day are shown on the page. Note that the transcript records only the actual messages typed by participants. System messages, such as those announcing the arrival and departure of people in the Chat, are not recorded.
Note the "Delete" hyperlink shown next to each message. These Delete links appear only on the teacher's display. As for most of the other modules, the teacher has veto power over which messages are displayed on the system.
As the teacher you can permanently remove any message from the transcript. To delete a message, click the corresponding Delete link and answer OK to the pop-up confirmation:

The purpose of the transcripts is to allow those who could not attend a chat session see what took place. Before long, however, students will figure out they can get a preview of what is going on in an active chat, before they enter the chat themselves, by taking a peek at today's transcript. This kind of lurking is not foolproof however. Because of the way the chat server works internally, messages recorded to the transcripts may not be made available the instant they are typed. That is, the transcripts can lag behind the actual conversation by as much as a minute or two.