My 0.02 here:
Live chat clients tend to be more 'gimme gimme gimme' oriented. They are more impatient. For this reason, I've actually thought strongly about tossing it. It doesn't add that much 'benefit' things that often.
Case in point:
Policy is to require a ticket for tracking purposes when a client wants a quote for work. This is in order to track the request, from beginning to end, for thoroughness.
When potential client starts a chat request for these things, and they're redirected to the contact form, it's typically an uphill battle. They don't want to do so, or say "I understand", and never do.
Either that, or the annoying "When will you activate my order, I just placed it like 5 seconds ago" chats. Oy vey...
From personal experience, live chat doesn't work terribly well.