Maybe I don't understand. But a (Check)Listbox, of course, does support scrollbars. The scrollbars are hidden if all items fit into the clientheight of the control, but when there are more items the vertical scrollbar does appear. A horizontal scrollbar appears when the width of the longest item exceeds the (non-zero) ScrollWidth.
The vertical scrollbar is replaced by a horizontal scrollbar when the Columns (count of columns) is 2 or more, and, again, when all items do not fit into the control rectangle.