From a little known mutator called "Capture the Chicken" in which only the person with the chicken can score, so you gotta kill whoever has the chicken so then you can have it and score... which is fun but not at all that.
Those of us who love monsters and put the "un" in "unreal" (not sure what that means) might have more demented ideas for this little feather duster.
Even if it were something so benign as having it wander around until it got close enough to peck someone's foot off... if you wanted to extract this chicken from the gametype, what would you do with it to make it more interesting?
I'm already picturing a stampede of these clucking horrors charging at me...