I would put the chicken in a cage and put a white hat on her head. Then put the cage in the panel and have a nice backup gyro. Gives a whole new meaning to 'caging the gyro'.
Since it is proven that migrating birds have magnetic sensors in their beaks, this might be the next step: replace the chicken with a migrating bird and have a heading reference as well. got to be cheaper and more reliable than an INS and GPS combined.
Now if we could find a migrating parrot, that would really open up some possibilities..