Yeah, thats easy.

Look in your templates starting with index.php template and look for something like:

PHP Code:
<?php the_time('M j, Y g:i A'); ?>
And change it to:

PHP Code:
<?php if($post->ID == 42){}else{the_time('M j, Y g:i A');} ?>
Where the number 42 is replaced with the number of the post id found in your admin that you don't want the date printed out.

Jimmy