Mechanically separated chicken—the stuff chicken nuggets and patties are made from—is what you get when you grind an entire chicken through a sieve, soak it in ammonia, and add flavor artificially. Also, it's pink.
UPDATE: We've found a video from a corporate manufacturer of the machines that executes this task (or at least part of the task; it's hard to know, it's in Chinese). Warning: This is totally gross an not for the faint of heart.
UPDATE 2: Here's an even better (?) video of the process, from a more industrialized facility.
UPDATE 3: Turns out, this was a little blown out proportion.