The only security for a chat room is turning the group mode on so that only students in a selected group can see each other in this chat room. You will find the group settings under Common module settings.

Remember that on the Course settings page, you can set Enrolment duration as Unlimited. This means that once a student is enrolled in the course, they are always enrolled until you manually unenroll the student. If you leave the course open to all the students who were ever enrolled, consider segregating your chat into groups. Then, create a group that includes only the currently enrolled students; this prevents previous students from giving away too much in the chat room.