The chicken chapter on 'Birds in the Ancient World from A to Z' , is quite an informative read.I'd love to read a book on the history of chickens.
I doubt that there were chickens in ancient Greece the time the 'Odyssey' was supposed to take place (12th century BC). Homer on the other hand lived on 7th century so himself might have encountered chickens, would have been strange to add them in his story though.you may, but it's there. As you note in your correction, chickens are present in Greece from the Cent.7 bc - and Homer is the source for almost anything thus dated (Hesiod is the alternative).