When you place a chicken coop on your farm you will get a popup message telling you that you found "Mystery Eggs". You will be able to share the eggs using the usual "Share the wealth" message.
All your friends will get the message that you found some Mystery Eggs and can click on "Hatch an egg" When you click on Hatch and egg you will receive one of the gifts listed below. If you hatch a White Mystery egg you will get a chicken coop if you do not already have one placed on your farm.
After you place chickens in your coop and they are 100% ready you will find occasionally find special eggs or "mystery eggs" when you harvest them.