Selection – Classifiable check boxes for classified options

A user profile form has a set of check boxes that determine which departments the user belongs to. The data is stored in a comma delimited list.

Now we have a new requirement: first order the list delimited by commas in the order of "primary department", then "secondary department", and so on. Once we have determined an interface for this, the users (or a designated representative) will re-select their departments in the corresponding order.

The answer in this UX.SE question seems to indicate that manipulating the UX checkbox would be confusing for users, so I can not determine how the interface should look for this feature.

How can I allow users to select departments in an order of primary, secondary, etc.?