Answer:
You go into the Uproar Forest where you beat the Mankey gang. When you start seeing Mankeys on the floors, look in all the rooms because the chestnuts are usually on the floors with Mankey in them. DON'T PEEL IT ONCE YOU GET THE CHESTNUT WHEN IN THE DUNGEON! It will fill up your belly and not do you any good. There is noone at the end of the dungeon, so once you get to the end, you'll exit the dungeon. After that talk to the Mankeys the next day. They will see your chestnut and ask you to peel it. Say "Yes" and they will work for you some more.