You are correct, articles are usually omitted in recipes. However, in the recipe you posted, you need to add more details. What are the quantities of mushrooms, onions and celery? How many chicken quarters did you use?
I don't know the specifics of your particular recipe, but here are some basic changes I would make (again, the quantities I list are totally arbitrary):
1 lb. chicken (in quarters)
1/2 cup chopped onions
1/2 cup chopped celery
2 large tomatoes, sliced
1 cup chopped mushrooms
1/2 cup flour
Moisten chicken parts with water and toss lightly in flour until coated. Put 1 tablespoon of oil into frying pan and heat until coated. Place chicken and vegetables into pan and cook until brown.