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