For starters, you could try gabbly.com. Just enter you website address and it will embed a chat box in your website. You can also try tagboards. You will just insert the code into your website and then it will appear there.
Thanks sanworld4all for initiating so nice topic. I was also looking for a chat box. Now our friends have suggested various options to create it. Thanks to them also. I will see it some time later. Thanks.
I tried CBox, it is a great enough chat box, and also simple in use. We just have to register for an account, and they will give you a code which should you fill into your website code. It also has much skins, friendly scripts.