It's helpful that you explained it wasn't in a school setting. That information would have shortened this thread greatly. Simply put, do what was already mentioned... use a Java or CGI chat that is installed on a web site and requires a password. This will let your students (who have a password) connect to the school server and they'd only be able to connect to it.
As you have stated this is so that students can communicate with each other, it is far from necessary to use mIRC specifically if there is a better solution.
Of course, there are other ways to allow chat to be run from a specific server and only give access to those who have passwords (or who have specific IPs). One example, which isn't really what I'd choose to do, but just shows that the ways you can do this "safely" are many, is to set up a Telnet BBS that includes chat. Students can log in, share files (sending in homework, for example), chat, etc. You could even allow them to play specific games (Doors) if you wanted to based on how much they chat (give points to play based on time online or whatever). Like I said, that's a rather unusual method. It's just there to show that you can do this many ways and are not limited to mIRC or even IRC.
