There are several ways to add chat to a website for free. The example below uses a chat applet that is on a existing chat server and is configured by parameters in the link itself. I have setup this link to create a chat room that while not registered (it can be) is fully functioning. Try It - A Simple Chat
Another way to do it is to use a free chat applet that can be installed on this site but connects to any IRC chat server the admins wish to connect with. This applet is called PJIRC Chat and is a more advanced chat applet then the first one.
To see a working example of PJIRC that I just installed on a friends website that also uses PHP like this site does you can go here - PeoplesChoices Chat
Note - there are no pop ups or other nasty things on the above site, it is a safe site. You will need to allow the security certificates to be loaded into your windows temp file when it asks because Microsoft Windows considers it a security breach any time you try to load an applet that is not on the same machine as where the service is being called from. In this case the chat server is not on the same machine as the webpage server so you must say YES for the applet to load.
The advantage of having the applet on your own server is that you are not dependant on a certain chat server to provide the service. You can have chat rooms on several chat servers and use the backup chat server in the event the main chat server goes down.
Another good reason for having the chat applet on your websites server is that you can connect it with your database if using PHP and have the nicknames you log in with on the website be automatically inserted into the chat applet for you.
Either way adding a chat these days is very inexpensive and takes less then a half hour to setup. There are other chat applets available, I use one that did cost a one time fee of $50 and it is a excellent chat applet but going that route is not always the best move.
I suggest using a free applet first and if chat becomes popular enough then you can always upgrade if you wish. I hope this has been of some service to the cause.