Try this, tested ,working fine..
some syntax problem and file name suffix you have to take care of.
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
<script src="jquery-1.10.2.js" type="text/javascript"></script>
<script type="text/javascript">
function loadLogRefresh() {
var FileName = $('#<%=lblFileName.ClientID %>').text();
$.ajax({
url: FileName,
cache: false,
success: function (html) {
$("#chatboxRefresh").html(html);
}
});
}
</script>
</head>
<body>
<form id="frm" runat="server">
<asp:Label ID="lblFileName" runat="server" Text="../ChatFiles/abc.htm"></asp:Label>
<br />
<div id="chatboxRefresh">
</div>
<br />
<asp:Button ID="btnRefresh" Text="refresh" runat="server" OnClientClick="loadLogRefresh(); return false" />
</form>
</body>
</html>