Limit post editor to only 1 category on edit post?

I have done a search through the forums and found many topics explaining how to show just one category on a page; this is not my question.

I’m wondering if it is possible (and if so, how?) to limit the author of a post on the Post Edit screen to only 1 category. For example, make those check-boxes radio buttons or at least uncheck the one that was checked upon selecting a new one. I realize this may not be possible since Category taxonomy is built in. If not Category, could this be accomplished with custom taxonomies?

Ideally I’d like to do this with the Category taxonomy. Thanks for any suggestions or pointers 🙂