There was one famous chicken that was beheaded (during a routine slaughter) just high enough to keep the brain stem intact. A clot coincidentally prevented death from blood loss, and it lived for two years as a touring attraction, before finally dying by choking. It spent most of its time attempting to preen and peck.

http://en.wikipedia.org/wiki/Mike_the_Headless_Chicken

It would be incredible if costly tissue like neurons just sat there doing nothing.

How big is a chicken's brain, anyway? As Jadael notes, the brain stem was intact. How much more is there to a chicken's brain? Also note that it hardly needed, say, its optical processing systems anymore.