// get years that have posts
$years = $wpdb->get_results( "SELECT YEAR(post_date) AS year FROM wp_posts WHERE post_type = 'post' AND post_status = 'publish' GROUP BY year DESC" );

foreach ( $years as $year ) {
// get posts for each year
    $posts_this_year = $wpdb->get_results( "SELECT post_title FROM wp_posts WHERE post_type = 'post' AND post_status = 'publish' AND YEAR(post_date) = '" . $year->year . "'" );

    echo '<h2>' . $year->year . '</h2><ul>';
    foreach ( $posts_this_year as $post ) {
        echo '<li>' . $post->post_title . '</li>';
    }
    echo '</ul>';
}