The audio tape/songbook I referred to above is "KidSongs Jubilee", performed by Nancy Cassidy and published by Klutz Press. Copyright 1990 by Nancy and John Cassidy.

The "Chicken" song is listed as "Traditional", but also says "Additional lyrics: Nancy Cassidy". I'm guessing that this may be a "G-Rated" version of the lyrics described by other posters above.

The words are almost exactly as I gave above. I was going to post an abc version of the music (which is given in the songbook), but I don't want to run afoul of the copyright. The first couple of lines, as I said, sound like the old standard "Jada".

By the way, if you have small children, I recommend this and any of the other "KidSongs" tapes.