If you look at the HTTP response headers on facebook's page, you'll see the following line:
content-security-policy: default-src *;script-src https://*.facebook.com http://*.facebook.com https://*.fbcdn.net http://*.fbcdn.net *.facebook.net *.google-analytics.com *.virtualearth.net *.google.com 127.0.0.1:* *.spotilocal.com:* chrome-extension://lifbcibllhkdhoafpjfnlhfpfgnpldfl 'unsafe-inline' 'unsafe-eval' https://*.akamaihd.net http://*.akamaihd.net *.atlassolutions.com;style-src * 'unsafe-inline';connect-src https://*.facebook.com http://*.facebook.com https://*.fbcdn.net http://*.fbcdn.net *.facebook.net *.spotilocal.com:* https://*.akamaihd.net ws://*.facebook.com:* http://*.akamaihd.net https://fb.scanandcleanlocal.com:* *.atlassolutions.com http://attachment.fbsbx.com https://attachment.fbsbx.com;
Facebook has a security policy disallowing scripts from domains that aren't part of this list, so I don't think you'll be able to load an external script from your extension.
If that header wasn't there, you would normaly be able to include scripts hosted on https://
protocol.