Dunedin police yesterday were hatching a plan to do just that.
Museum staff noticed the fossil was missing from the ground-floor shop early on Tuesday. Security footage showed a man taking the egg.
Yesterday morning, the egg was left in a supermarket shopping bag at Dunedin Central Police Station while the main counter was unattended.
Senior Sergeant Bruce Ross said a person resembling the man who appeared in the museum's footage of the theft was caught on the police station's security cameras dropping the egg off about 8am.
It was valued at $1700.
Museum development and planning director Clare Wilson said it was great to get the egg back, but the museum would still like to see the person who took it apprehended.
Police returned the egg to the museum yesterday and reviewed the security footage.
Snr Sgt Ross said police had received several helpful pieces of information from the public and were following a positive line of inquiry.