Add class to first post in WordPress loop. A snippet for the functions.php.

gistfile1.txt

add_filter( 'post_class', 'add_class_first_post' );
function add_class_first_post( $classes ) {
    if ( ! is_admin() ) { // add any conditional here (ex. homepage only), this might not be needed
        global $wp_query;
        if( 0 == $wp_query->current_post )
            $classes[] = 'first'; // class name
            return $classes;
    }
}