If you log into Roblox: Grow A Garden after the event is already live, you won't receive the Chicken Zombie. As such, the only way to currently get this pet is by trading.

Roblox Grow A Garden has many things you can do, including apparently getting a chicken...who is also a zombie. Go figure.

Roblox Chicken is an interesting experience that tests your movement skills at every turn. Your primary objective is to steal the eggs and survive without being caught by the chickens.