Coat chicken lightly with flour. Heat oil in a wide saucepan over medium high heat. Fry chicken pieces briefly, turning to brown evenly. Add onion and celery; cook 1 to 2 minutes. Stir in wine and chopped tomatoes. Season with oregano, and salt and pepper to taste.
Cover, reduce heat, and simmer gently for 30 minutes, turning pieces once.
Pour in balsamic vinegar and mushrooms, and cook further 5 to 10 minutes.
Great recipe. I used boneless thighs fried them in olive oil and garlic. I also added thyme. Very flavourful, but next time I will double the sauce portion. I didn't bother with peeling the tomatoes...but I did seed the tomatoes as the recipe called for. If there was a difference to peel the tomatos, i'm not sure what benefit that would give me, because the dish was excellent without the extra work in peeling the tomatoes. - 18 Jul 2008