The easiest approach (not taking into account using all ready existing plugins) would be to use Ajax and a database. This means that the protocol will be HTTP/HTTPS if you want to implement it into your company's website.
The client and server side depends on how you want the chat to function. Try building something similar to IRC with one room for example.
create a database table which will hold the chat
on the client side implement a method which will send a message with Ajax and also recieve all messages posted
for the server side all you need is something which will store the new message and provide them when requested from the client
As I said, this is just a quick example, if you want a more complex chat system you will have to do a bit of research.