Technically it should work but why are you putting a div into an anchor? If it is so you can make the anchor have a specific appearance, it may be easier and less buggy to make your list inside a div, then but the style attributes of your <div> apply to the anchor inside the list. For example:
(Style.css)
div#yourdiv ul li a
{
/* Put your properties here */
}
(index.html)
<div id="yourdiv">
<ul>
<li><a>Your anchor text here</a></li>
</ul>
</div>
-JL Griffin