At the moment the limit is 1 chicken coop.
But you can get 2 coop with a litle trick.
1. You must sell chicken coop (if you have it) 2. You must hatch mystery egg and because you wont have a coop you will get one (you will find it in gift box but dont use it right away) 3. Go to the market and buy chicken coop 4. Then go to the gift box and use a gifted coop