Can somebody tell me exactly where you place this code in The Loop?
<?php
global $wpdb;
$numposts = 1;
$rand_posts = $wpdb->get_results("SELECT * FROM $wpdb->post2cat,$wpdb->posts,$wpdb->categories WHERE
$wpdb->post2cat.post_id = $wpdb->posts.ID and $wpdb->post2cat.category_id = $wpdb->categories.cat_ID and $wpdb->posts.post_status = 'publish' and $wpdb->categories.cat_name = 'featured' ORDER BY RAND() LIMIT $numposts");
foreach($rand_posts as $post) :
setup_postdata($post);
?>
Template tags and whatnot go here.
<?php endforeach; ?>