It's not exactly a song, and i don't know why people call it that. You may have noticed that after a chicken lays an egg she will cackle for a while afterwards. It sounds like:
"BAWK BAWK BAWK BAWK BUH-KAWK!!!! BAWK BAWK BAWK BAWK BUH-KAWK!!... repeat repeat repeat...
It gives one the impression that the hen has just gone through a very distressing ordeal. I seriously don't know what put it into their heads to call it a "song".
Actually, chickens make noise also before they lay the egg. This one is actually slighty more of a song:
"WAAAAAAA-WA-WA-WA-WA-WA-WA-WA" (the "wa-wa's" go on for a while) and then it continues: "WAAAAAAA-WA-WA-WA-WA... et cetera"