How to setup two checkboxes in the Web UI, but only one can be checked at a time?

I have two checkboxes on the Web UI, each one is a Boolean virtual attribute. I would like to make the Web UI uncheck the opposite box when one is checked. I'm assuming I use EDS_EPI_UI_RELOAD_EPI_BY_RULE, but I'm just going in circles trying to implement that so as the user checks boxes, the opposite unchecks itself. I'm doing this to try and get a "radio button" feel, but with checkboxes (because I don't believe custom radio buttons are available).

When the page loads, both boxes are unchecked. I check BoxA. Then, if I check BoxB, BoxA should uncheck itself and vice versa. Essentially, performing like a radio button.

Any ideas out there? Is it even possible?