The Chicken Patch resource is introduced with either the All Keyed Up or Eggs-istential quest (depending upon which you hit first). As with the Cow Pasture and the Milk it produces, the Chicken Patch and the Eggs it produces will be a huge part of the game for pretty much its entire length.
Available at level:
First: 2,500 royal coin, 30 crowns thereafter
Time to build after purchase:
Maximum number per kingdom: