The Tarnished Crown is an item used to unlock the Don't Starve: Shipwrecked character, Wilbur. It has a 10% chance to drop when any Prime Ape dies or any Prime Ape Hut is destroyed. The drop will not be available if Wilbur is already unlocked or a Tarnished Crown already exists in the world.
If Wilbur is not unlocked yet, he can be found on a Raft in the Shallow Ocean. Giving Wilbur the Tarnished Crown will unlock him.