The problem with your solution is you're putting a scrollbar around a ListBox where you probably want to put it inside the ListBox.
If you want to force a scrollbar in your ListBox, use the ScrollBar.VerticalScrollBarVisibility attached property.
<ListBox
ItemsSource="{Binding}"
ScrollViewer.VerticalScrollBarVisibility="Visible">
</ListBox>
Setting this value to Auto will popup the scrollbar on an as needed basis.