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I used free trial version of eAssistance Pro live chat on my E-commerce website and wasfully satisfied with its features & functionality. It's easy to install and operate, secure reliable and low cost software. We can analyze traffic and monitor real time visitors by using it.
I too can vouch for LiveZilla. I used it a while back on one of my sites.
I currently don't offer live support now because I'm more mobile answering tickets via my smartphone, etc. If I was solely in an office during the day, then I'd offer it to my customers. But for now, we just use tickets.
Live2Support is one of the best for small and mid size business websites. 15 days free trial. Go for paid version when you satisfied 100%. Plenty of very advanced features (Analytics, Pro-active chat invitation, push notification etc.)