NOTE: Your LiveAgent installation must be available via HTTPS://, because Facebook allows to load external source only through secured links, more exactly from sites that use good quality SSL ceritficates.
Self-signed certificates are not accepted by Facebook. NOTE2: Your Facebook page must have at least 2000 likes in order to be able to add the static HTML page. This is unfortunately a Facebook policy and you won't be able to add LiveAgent widget if your page doesn't have this number of likes.
This is possible only via a special application called "Static HTML: iframe tabs".
log in to your facebook account by which you manage your facebook pages
You will be redirected to your Facebook page with new application tab titled "Welcome" with a large green button "Set up tab"
Click the "Set up tab" button to edit the custom tab where you can paste thechat button (or contact form) integration code. Please keep also some text in the edit area, because it won't work if there is only the the integration code.
click Save & Publish
click View on Facebook. The custom tab in your facebook page should look like this:
If you wish to change the name of the tab from "Welcome" to something else, you can do it in the "Edit tab" by clicking "Actions" and then "Edit name and image"