You can do this with PHP. Flynn helped me out when I wanted to show posts from all categories on the front page EXCEPT from 2 categories, Obituaries and Letters to the Editors. I wanted them to show only in the left sidebar as separate "Recently In....." widgets.
I put this in the Style and Edit Center Column/Content Above the Loop section:
<?php if (is_front_page() && !is_paged() )
$posts = query_posts($query_string . '&cat=-15,-80'); ?>
The -15 and -80 means "don't show posts from these categories". The clunky way to do what you want would be to put all of your categories EXCEPT the one you do want in there with the minus sign. The elegant way would be with the proper PHP code.