You need to add the code in the sidebar template file, not the css stylesheet. Go into Admin >> Appearances >> Editor >> right_sidebar.php
and add this code directly BELOW the <ul>
tag at the top of the page:
<li><a href="#"><img src="<?php bloginfo('stylesheet_directory'); ?>/images/XXXXX.jpg" alt="" /></a></li>
Then upload the image to the images directory of the theme and change the XXXXX.jpg
to your image's name. Also insert URL in place of the #
sign at the beginning of the code.
Adding the code there will insure that it is always showing regardless of whether or not you use any widgets.