It is currently possible to block the Chat elements within Facebook using the Web Security.cloud service.
But firstly a disclaimer:
*The following may become unreliable due to the very dynamic nature of Facebook. The URLs Facebook use may change without any notice rendering the following ineffective*
These were tested on Monday 9th January 2017.
The solution will render the following sections within Facebook unusable to the end user.
In order to block the use of Facebook Chat you will need to create a new Block and Log rule within the URL Filtering section.
Step 1 - Create a new URL rule giving it a name and setting the action to 'Block and Log
Step 2 - You can choose to apply the rule to a specific group of users via the Group tab or skipping this tab will apply this rule to all
Step 3 - Navigate to the 'Specific URLs' tab and input the following URLs:
You can also add the following URL to the list. This will block the standalone Messenger website.
Step 4 - Once these are added into the new rule, save the rule. Then activate it by clicking on the word 'Inactive'.