Allow WordPress to Use Permalinks on Amazon EC2

On Amazon EC2, even with a properly configured HTACCESS file, permalinks will not work, resulting in 404 error pages. While this is documented, I found it hard to find:

Look for the heading “To allow WordPress to use permalinks”. In your Apache configuration file, within the section that starts with <Directory "/var/www/html">, change AllowOverride None to AllowOverride All. If your Apache configuration file does not include this section, add it. Restart Apache and permalinks should work.