I did something that should be able to be adapted to a div as well.
HTML
<td>
<%# (Eval("Name").ToString().Length > 65) ? Eval("Name").ToString().Substring(0, 60) + "..." : Eval("Name")%>
<span class="showonhover">
<a href="#"><%# (Eval("Name").ToString().Length > 65) ? "More" : "" %></a>
<span class="hovertext">
<%# Eval("Name") %>
</span>
</span>
</td>
CSS
.showonhover .hovertext { display: none;}
.showonhover:hover .hovertext {display: inline;}
a.viewdescription {color:#999;}
a.viewdescription:hover {background-color:#999; color: White;}
.hovertext {position:absolute;z-index:1000;border:1px solid #ffd971;background-color:#fffdce;padding:11px;width:150px;font-size: 0.75em;}
For a more in-depth discussion, see my post: