If I choose to lose my headgear due to Income Tax, does that qualify as an event that would take the chicken with it?
The cards say:
Income Tax: Discard one item of your choice. Every other player must now discard an item or items, totaling at least as much value as the item you discarded. If they don't have enough to pay the full tax, they must discard all their items and lose a level.
Chicken on your head: -1 to all die rolls. Any Curse or Bad Stuff that removes your Headgear will take the chicken with it.