Facebook Chat by Elfsight is the fastest way for your clients to reach you and get their questions answered. Stay available live for users in their favourite messenger 24/7. Integrate Facebook Chat on your website and set it to appear on specific pages or for a certain groups of visitors, choose start-chat triggers, create your own welcome message, choose icons and more. With the help of Facebook chat on your site, you will stay connected anytime and from anywhere.
Demo: https://codecanyon.net/item/facebook-chat-wordpress-facebook-chat-plugin/23878195
source http://www.codelist.cc/plugins/241496-facebook-chat-v120-wordpress-facebook-chat-plugin.html