First, visit Facebook
Jump to the end of this section and straight to the download page with this link.
Navigate to the settings page in the menu bar on the top right.
Navigate to the settings page for your "Settings & privacy".
On the left pane, select "Your Facebook information"
Then in the main pane, click "View" for Download your information.
Select your time period, "JSON" format and "Low" media quality for compatability with DoubleText.
Then click "Deselect all"
Then select "Messages" only.
Then click "Create File"
You'll receive an email once that's done. Click the link in the email to be brought to the next page.
In your available copies section, there should be a download button for your latest copy.