If you look at MSDN on CheckedListBox(
here[
^]), you will find under Properties:
"DataSource Infrastructure. Gets or sets the data source for the control. This property is not relevant for this class."
And:
"Note You cannot bind data to a CheckedListBox. Use a ComboBox or a ListBox for this instead. For more information, see How to: Bind a Windows Forms ComboBox or ListBox Control to Data."