Live chat, for me, is a requirement! But a website having a Live Chat button doesn't mean anything if nobody is ever around, or it's always offline.
We ran 24x7 live chat for over 15 years and it was the best investment. Not just sales chat, but tech support chat. If support took longer than 15 minutes or we needed to document it, then we asked clients to put in a ticket, but Live Chat is what our customers came to expect and depend on.
Today, I use a host that offers live chat. I have another that only offers Live Chat for Sales, but usually when I have a problem, I need an answer, and not a sales question.
If you can man the stations and have the support staff to handle it, then Live Chat is a great option. Even running it just 9-5 while you're around, is a benefit. But longer chat hours would be recommended.
If you can get your ticket responses in less than 15 minutes (and I mean REAL responses, not just "I'll look into it"), then Live Chat should be your next option to offer.