We had live chat on our website for quite a while.
It was ok while I was in the office to man it but as we got busier and I was out of the office more, I thought it looked less professional to have live chat showing 'offline' so we removed it.
The best thing for us is call divert, all calls diverted to my mobile, so no matter where I am, they still get the same call response as they would if I was sat in the office.
Emails also come through to my mobile and always get a response within 2 hours.
Would I allow someone else to run my live chat for me? Not a chance!
I have used telephone answering services with operators saying 'I'm sorry the person you need to speak to is unavailable, can I take a message for you?'
I've also been on to sites that have 'Live Chat' operators who leave you feeling suicidal with frustration because they haven't got a clue about the business they are representing.
My mobile phone is my mobile office ... and it doesn't cost me any additional costs.
I'm afraid I wouldn't trust a stranger with no knowledge of our business to be the first point of contact with a potential or regular customer. It takes years to earn a good reputation and seconds to lose it.