I had to do a bit more searching but your suggestion sent me in the right direction, so thanks @elliot
Here was my final code:
<?php
global $post;
$the_post_ID = $post->ID;
?>
<?php foreach ( $posts as $post ) : ?>
<li<?php if ( $post->ID == $the_post_ID ) echo ' class="current"'; ?>>
<h3><a href="<?php the_permalink(); ?>" title="<?php echo get_the_title( $post->ID ); ?>" rel="bookmark"><?php the_title(); ?></a></h3>
</li>
<?php endforeach; ?>
