According to the official Zynga Blog for FarmVille 2, the Prized Chicken Coop is theoretically available once you unlock Level 6, however I was not offered it for placement by the server until after I unlocked Level 8.
As we covered earlier the Prized Animal Structures offer more than simply a place to put your Prized Animals in a conveniently placed group, but each has additional elements that broaden the value for each of the different Prized Animal types as well as improving the overall game conditions.
For example your Prized Chicken Coop, in addition to providing you a place to put your Prized Chickens, also offers you the following expansion elements:
When the game prompts you to place your Prized Chicken Coop it is not actually having you place the Coop, but rather the Prized Chicken Coop Construction Project, which is completed in two stages.
The first stage requires you to request the building materials that are necessary to complete the construction project, while the second stage requires you to obtain the volunteer labor of your friends and neighbors in the actual building of the structure.
The resources required to build the Coop are:
The Prized Chicken Coop is placed within the confines of the Animal Pen that we created after unlocking the sixth contiguous Farm Section, as we intentionally built the Animal Pen so that it was large enough to contain the various farm animal-related buildings in order to make the maintenance and the presence of our farm animals as convenient and orderly as possible.