White - Chapter 1-2. Just before you head into the building with the lady in the black dress head up to the roof of the building which has the shotgun. Should be a chicken up there, if not he's already roaming about. Drops as white egg on Normal difficulty.
Brown - Chapter 1-2. Same as "white" but play on Amateur.
Gold - Chapter 3-1. Middle island on the map, the "chicken farm." Arrive and wait a moment, chicken should give a little cock a doodle do and drop it.
Rotten - This drops randomly later in the game from Chapter 4-1 onwards off defeating enemies