Basic HTTP authentication uses a challenge/response scheme to authenticate users attempting to access a password-protected page. The challenge process begins when the user requests a file from a Web server. If the username and password pair is valid, the protected file will be displayed to the user.

A simple PHP script can mimic the HTTP authentication challenge/response system by sending the appropriate HTTP headers that cause the automatic display of the username/password dialog box.

They give all of the code to make it possible. However, it does make use of the globals that you might not have access to if your hosting provider has them turned off. In that case, you can use $_SERVER['PHP_AUTH_USER'], $_SERVER['PHP_AUTH_PASS'], and $_SERVER['PHP_AUTH_TYPE'] instead...

Thanks to Nexen.net for the pointer.