You need add a width to your ul container. Remove floats and left rules from your containers and do instead:
#centeredmenu ul {
position : relative;
width : 840px;
margin : 0 auto;
overflow: hidden;
}
#centeredmenu ul li {
position : relative;
float: left;
}
Here is an edit based on your example http://jsfiddle.net/ETsR8/