I thought of Chaos: A Fantasy Adventure, Connections, and Bioscopia, but I don't see a chicken in any of the screenshots -- or anything remotely resembling a chicken. Of course if the chicken is only on screen occasionally, it may not have gotten into the screenshots.
Armed and Delirious (aka Dementia and Granny) had a chicken in it.
At least the walkthrough mentions a chicken.
Here are some screenshots.http://www.mobygames.com/game/windows/armed-delirious/screenshots
How old is the game? If it's less than 5 years old, could it be a casual game? Casual games often have little mascot helpers, and there may be one with a chicken.