If this is a Windows Forms Application then I don't think there is a simple solution. However if this is a WPF Application in your Loaded event just change the listBox BorderBrush property (e.g.
listBox1.BorderBrush = Brushes.Green
).
or for Asp.net in the Page_Load event:
ListBox1.BorderColor = System.Drawing.Color.Green
Note: If you want to do this in another event say a Button Click event it will cause the page to refresh. If you do not want this to happen you will have to use AJAX.