I've posted before about ways to cook an old chicken:

Stew it for eight hours.

Cut the raw meat off the bones and grind it for use in potstickers, sausage, etc.

Both of those methods work (especially the second one), but I recently discovered that neither is the traditional way to turn that hen who no longer lays well into dinner.  It turns out that old chickens were actually preferred by many cooks until recently since chickens over a year old have more flavor.  These chickens were sold as "fowl" or "stewing chickens" and were used to create chicken soup, chicken stock, chicken salad, and chicken pot pies.

Both of the methods I've used to cook old chickens in the past break apart the tough, stringy fibers that inevitably form if you cook a fowl in boiling water, but you can prevent these fibers from forming in the first place by using moist heat that never raises the temperature of the chicken above 180 degrees Fahrenheit.  I tried out two methods, my favorite of which was to put two cups of water in the bottom of a Dutch oven (or other covered roaster) and bake at 325 degrees Fahrenheit.  Alternatively, you can get the same effect by cooking your chicken in a covered pot on the stove as long as you make sure the water never boils, but I thought it was more difficult to keep the liquid at a simmer in that situation.  Crock pots are reputed to raise the temperature too high.

Either way, you'll want to cook your fowl about an hour per pound, removing the white meat as soon as it's done and then stewing the rest of the chicken a bit longer.  Cooked in this manner, the meat will only be a tiny bit tougher than meat from a grocery store chicken --- chance are, no one will notice if you don't tell them.

I consider chicken stock to be the most efficient use of a chicken, especially at this time of year when I'm turning my garden into soup for the winter as fast as I can.  To make the stock, I removed the breast after two hours, then added more water and simmered the carcass for a few more hours until it was easy to peel all of the meat from the bones.  Then I tossed the stock and meat back in the pot with all of the fixings for harvest catch-all soup.  One old chicken made a gallon and a half of condensed chicken and vegetable soup, enough for two dozen winter meals.  Now that's a good use of an old chicken!