Intercom (https://www.intercom.com/) is by far one of the best companies for this out there. Saying this as Marketing Director who has gone through half a dozen top vendors over the past 5 years. This being said Intercom still requires reps to manage the messages.
If you're looking for something free I've been running into an increasing number of sites that use tawk.to (https://www.tawk.to/). Again here you need a rep to manage the chats, but you have the option to hire a chat agent very cheaply - might be worth exploring.