In order to chat on Facebook, you will need to access the main Facebook website and not the faster mobile Facebook site.  On a Google search for ‘Facebook’, the Mobile website version is denoted by a green mobile phone icon.

On the main Facebook website, you will need to click on the speech bubble in the bottom right-hand corner.
You may need to allow pop-ups before this will work successfully.
To allow pop-ups, open Internet Explorer and go to View > Internet Options.  Then click on the Popups tab.  Remove the tick from the ‘Block popups’ tick box and click OK.