Well, I found it hard to believe that Cash actually recorded this, so I did a quick google, and, seems like he did. I even found a few videos...

According to a well-known Cash forum poster named MHIC the original title of the song was "Brain Transplant" and it was recorded in 1984 in the "Billy Sherrill sessions".

And the en.Wikipedia entry on Cash has this to say about the song: "He realized that his record label of nearly 30 years, Columbia, was growing indifferent to him and wasn't properly marketing him (he was "invisible" during that time, as he said in his autobiography). Cash recorded an intentionally awful song to protest, a self-parody. "Chicken in Black" was about Johnny's brain being transplanted into a chicken. Ironically, the song turned out to be a larger commercial success than any of his other recent material." No citations directly linked to that part though, sadly...

Thought this might be of interest to some folks...

Jesse Weinstein