I agree that most customers don't want to wait for their ticket to be addressed. They would rather have some sort of more instant acknowledgment. Live chat also provides comfort. They know a real person is aware of the issue and is working in real time to resolve it. The more quickly an issue is resolved, the happier the customer will be.

Live chat is very important for customers that need a quick resolution or have some question or clarification about the service. The ticket system is important too especially for the company since they can monitor the issues at hand and also how well the support group is doing its job.

Good live chat system can replace tickets in most cases, but not everytime. Users definitly should have a possiblity to ask a question in one click, because it shows the quality of your service and means you really care. So it's better to use a live chat at the first line and have a ticket system as an additional variant for special queries.

Check kayako and livechatinc live chats, they also offer this feature

For starters, providing live chat support can be tedious and expensive. Imagine not having the necessary number of staffs required for the task or hiring too many staffs just for live chat.. It makes no sense for fresh start-ups.. It's a nice feature to have for established hosts though.

We actually use our Live Chat for both Sales and Support relations, and at times we do Billing Relations but our Sales and Support is 24x7x365. I personally think it's a great idea to have both if you have the man power, but it's really up to your business structure and if you have the income or means to be on the live chat for hours a day.

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