mkdir() not working

This should be simple, but it's not working. I'm trying to create a dir in the public_html dir using the following php script

PHP:

// create the user directory
$dir = '/home/site/public_html/'.$username; 
$make = mkdir($dir, 0644);
if(!$make) {
    die('Can not create the folder for this user.');
}

However, I keep getting permission denied errors.

This is a brand new installation. Is there something I should be looking for?