Livezilla's good as long as your comfortable including all the server coding/database needed to run it. There are more than enough external providers as well; just depends where you want the db to reside.
I'd vote for LivePerson and Kayako's Live Support suite. They've got all the features you would need and are really user-friendly, especially LivePerson.
__________________
▌Jason @ InspiroHost :: Blog Hosting
▌Servers in New York, Chicago and London. Try our Business Hosting.
▌cPanel, Shared Web Hosting, 99.95% Uptime Guarantee, Money Back Guarantee.
__________________ www.AYKsolutions.com - Atlanta, Jacksonville, Chicago, Los Angeles
From Shared to Dedicated - High bandwidth plans & VPS available
Professional. Painless. Polite.