The tiny hen in my avatar, who was always good-natured and always let me pick her up, turned into a homicidal maniac once she settled on the nest. Things did not improve when her chick hatched. She takes on anything that comes near her chick including my huge Orp roo - all the other chickens are...
My broodies are always mean. Wait until she gets off the nest and you try to pick up one of her chicks!
I would definitely get the dead one out of there right away.
You may not want to take her off the nest if a few are due to hatch, she may not go back on it, then you've got a problem. You...