Remove core from tomatoes and cut a cross in the opposite end. Put into boiling water for a few seconds to loosen skins. Peel, cut in half crosswise and squeeze out seeds. Chop and set aside. Wash and dry chicken; cut into serving pieces, discarding neck, back and wing tips; dredge lightly in flour. Heat olive oil in a large saute pan, and brown chicken lightly on both sides. Add onion and celery and cook for 2 minutes. Add the wine, oregano and tomatoes; season with salt and pepper, cover, and let simmer gently for 30 minutes, turning chicken once. Add the Balsamic vinegar and mushrooms; cook another for 5 to 10 minutes. Check seasoning and serve with hot cooked rice. Serves 4.