So, one of(if not the most) popular post on my site is a post I wrote on how to disable Facebook Chatheads. This was over a year ago, and I decided to revisit it.
It seems like now the way to turn this off is from the Facebook app itself.
From the Facebook application, goto Settings -> App Settings(under Help & Settings)
Scroll to the bottom and click on Messenger Settings under Chat Heads
Finally, switch to OFF.
And you are done!