With the help of the Template Hierarchy article, determine what Template is displaying your posts (could be index.php). Then edit that Template and delete the code that displays that post.
The code will look like:
<?php $my_query = new WP_Query('showposts=1');
while ($my_query->have_posts()) : $my_query->the_post();
$do_not_duplicate = $post->ID; ?>
<div class="post new" id="post-<?php the_ID(); ?>">
<h2><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title(); ?>"><?php the_title(); ?></a></h2>
<div class="info"><div class="comments"><?php comments_popup_link('0 Comments', '1 Comment', '% Comments'); ?> | This entry was posted on <?php the_time('M d Y'); ?> <?php edit_post_link('Edit', ' | ', ''); ?> </div></div>
<div class="content"><?php the_content('Read more »'); ?></div>
<div class="meta">
<div class="tags"><?php the_tags('', ', ', '<br />'); ?></div>
<div class="cats"><?php the_category(', ') ?></div>
</div><!--meta-->
</div><!--post-->
<?php endwhile; ?>