There are atleast several ways to do it. In general if you are not using native widget placement you should insert javascript at the page footer before closing </body> tag.

So here is the ways to do it correclty.

Installing wordpress plugin to insert header and footer scripts.

http://wordpress.org/plugins/insert-headers-and-footers/ - here is plugin for that.

Follow tutorial

In general this tutorial is dedicated to google analytics. But instead of pasting google analytics code just paste Live Helper Chat generated code.

http://www.wpbeginner.com/beginners-guide/how-to-install-google-analytics-in-wordpress/