Can I create a parent-child relationship within the same form via a Lookup field?

Can I create a parent-child relationship within the same form via a Lookup field?

For example:
Widgets A and B have no parent. The Parent lookup field is therefore empty.
Widget C is the child of Widget A. The Parent lookup field contains Widget A.

Widget D is the child of Widget C. The Parent lookup field contains Widget C.

How do I create a Widget form that allows this relationship to be contained in a "Parent" lookup field? When I try, I am not offered the "Widget" form as a source of the lookup data for the field, only the other forms in my application.