In Delphi, how can I make a button appear on top of a TCheckListBox?

Question

We want a list box with check boxes and formatted text. We get that using a TCheckListBox in owner-draw mode.

But we would like to also have a button appear at the right end of the selected row. Just adding a button (TSpeedButton) with the CheckListBox as the Parent doesn't get drawn correctly.

Does anyone know how to do this?