Here is a way:

// listen for post being published
add_action(\'publish_post\', \'dreis_random_featured_image\');

function dreis_random_featured_image() {
    global $post;

    // find one random image    
    $args = array(
        \'post_type\' => \'attachment\',
        \'post_mime_type\' => \'image\',
        \'post_status\' => \'inherit\',
        \'posts_per_page\' => 1,
        \'orderby\' => \'rand\'
    );

    $random_image = new WP_Query($args);

    foreach($random_image as $image){
        // set as thumbnail
        set_post_thumbnail($post->ID, $image->ID);
    }

    // reset loop to avoid weirdness
    wp_reset_query();
}