Now I’ve never claimed to be a WP pro, but I have figured out how to make this work.  Below is the code to get it done.  The trick is the first line, the required wp-load file.  That’s what lets you use some of the wp functions outside of the loop.

<?php require( 'path_to_blog_root/wp-load.php' );
$getpostq=mysql_query('SELECT ID,post_title FROM wp_posts WHERE post_status="publish" ORDER BY post_date DESC LIMIT 1');
if (!$getpostq) { die('Error selecting info: '.mysql_error()); }
while ($getpostr=mysql_fetch_array($getpostq)) {
$post_title=$getpostr['post_title'];
$pid= $getpostr['ID'];
$postlink=get_permalink($pid);
echo "Recent Discussion: <a href=\"$postlink\" title=\"Link to $post_title\">$post_title</a>";

If you also want the post date, you can add these lines:

<?php require( 'path_to_blog_root/wp-load.php' );
$getpostq=mysql_query('SELECT ID,post_title FROM wp_posts WHERE post_status="publish" ORDER BY post_date DESC LIMIT 1');
if (!$getpostq) { die('Error selecting info: '.mysql_error()); }
while ($getpostr=mysql_fetch_array($getpostq)) {
$post_date=$getpostr['post_date'];
$post_date=date('F j, Y', strtotime($post_date));
$post_title=$getpostr['post_title'];
$pid= $getpostr['ID'];
$postlink=get_permalink($pid);
echo "Recent Discussion: <a href=\"$postlink\" title=\"Link to $post_title\">$post_title</a>%lt;i>($post_date)</i>"; ?>

By the way, if you have a better way to do this, I’d love to see it.