You're using an outdated version of jQuery, change to a newer version and it will work in Chrome.
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
Also just a small edit to your code:
$(function() { // DOM ready shorthand
$('.mydiv').hover(function( e ) {
$(this).stop().fadeTo(300, e.type=="mouseenter"?1:0.5);
});
});
Without jQuery, in CSS3
.mydiv{
/* your styles here */
opacity: 0.5;
transition: opacity 0.3s;
}
.mydiv:hover{
opacity: 1;
}