The Hen House is the Collection Quest for Chickens, and features a set of rare eggs as its basic function - or rather it features a set of rare eggs for you to collect. The rare eggs are:
There are three classes of eggs, those being Uncommon, Rare, and Ultra Rare, with a total of five specific eggs making up the entire collection as follows:
When you complete this collection, you will receive a reward of a rare chicken - the Polish Silver Laced Chicken.
Construction of the Hen House requires the following resources:
You will need to request most of these from your mates -- the Wood Planks you likely already have some of from your feed and inbox, since that is a popular free gift selection for most players.
The Egg Collection has specific Chicken population requirements, or rather specific Adult Chicken population requirements.
You will have to maintain the minimum required number in order to keep the timer for the Collection running - the game is pretty in-your-face about letting you know when you have not maintained the required number so knowing that will not be an issue.