The question to ask yourself is will you have staff members be able to monitor and be responsive to this all the time. Nothing is more frustrating then offering Live Chat then having it show a "Leave a Message" or "Chat is Offline" for members. It's a missed conversion chance if you can't "man the phones".
The following is a list of companies that provide similar services (in no particular order) of a flyout/popup chat system that allow you to communicate directly with customers.
Contact us today if you want to explore setting one of these services up.