Place all ingredients in a large stock pot.  There's no need to peel the carrots or discard the ends.  You are going to strain all the veggies out of the stock anyway.  You can even leave the peelings on the onions.  Just make sure your celery is cleaned well.    Bring to a medium boil with the top on and cook for 15 minutes.  Remove from heat, keep covered and let stew in it's own juices for at least one hour.  Then, you can remove the chicken and strain out the veggies.   If you have the time, place the stock in the refrigerator overnight and all the grease will congeal making removal easier.  This stock freezes well.