How to make a Wordpress site private with only Facebook login?

I want to make my Wordpress site totally private unless the user logs in with Facebook. So, the users have to login via Facebook to enter/view the site.

It is a demo site so I am not worried about "but what if the user doesn't have a Facebook account".

I have searched for Facebook plugins but my results all seemed to focus on posting to Facebook.

Is this possible via a plugin?

via Chebli Mohamed