And please, if you do this, always let the customer initiate the chat session.
I find few things creepier than having a chat window suddenly pop up on my screen with a "helpful" customer service rep offering to assist me when all I was doing was browsing the site.
As Karri said, live chat may work for you, it may not. Depends on your visitors and what you're selling.
Keep in mind, too, it does require a time commitment. If you have a button that offers "live chat" but every time a customer visits your site it says live chat is closed, they're going to start to wonder if you really do offer it or if you just put a button there to make it seem as though you do (not to mention that a "closed" live chat can't do the job of answering questions for the customers.)
So you'll need to take into account the "opportunity cost" -- what else might you potentially be doing instead of making yourself available for customer chats? Could those "other things" benefit your business more than live chat?
If you can get a free/low-cost trial, it might be worth giving it a try to see what happens.