If you want to increase engagement with your website visitors, then adding live chat may be the ticket.
Not only is it an effective way to communicate, but it also gives your visitors a sense of availability.
Since posting this, I have started using ConvertFox on this website because I like how it's focus is not on live chat per se, but simply chat.
When someone requests a chat, they are notified of my response time and asked to leave an email address. When they do, ConvertFox will email them when I respond and they can then return to the website to further communicate.