I believe it looks as you mentioned but still not sure why it would render the chart empty when the second updatepanel is brought into the picture.
<asp:Button ID="btnSearch" runat="server" Text="Search" OnClick="btnSearch_Click" />
<asp:UpdatePanel ID="UpdatePanel1" runat="server" UpdateMode="Conditional">
<ContentTemplate>Gridview Here</ContentTemplate>
<Triggers>
<asp:AsyncPostBackTrigger ControlID="Chart1" EventName="Click" />
</Triggers>
</asp:UpdatePanel>
<asp:UpdatePanel ID="UpdatePanel2" runat="server" >
<ContentTemplate>Chart Here</ContentTemplate>
<Triggers>
<asp:AsyncPostBackTrigger ControlID="btnSearch" EventName="Click" />
</Triggers>
</asp:UpdatePanel>