Good Chatbox Plugin

Good Chatbox Plugin

Hello - 

I want to build chatbox capabilities for my own website. Does anyone here have any experience with chatboxes? If so, is there a plugin you would recommend?

Also - can you give me a quick summary of how chatboxes work on the backend? When site visitors enter something into the chatbox, I'm assuming it's pushed through php? But, how is the response handled? I want live capabilities, where a chatbox pops up on my end if a site visitor chooses to start a chat.

Thanks in advance - Pavilion