Season chicken breasts with salt and pepper, then dredge in flour until completely coated. Heat 2 tablespoons oil in a Dutch oven and fry breasts until lightly browned, about 5 minutes on each side. Remove chicken from pan and set aside.
Add remaining tablespoon of oil to the pan and saute the onions for 2 minutes. Stir in the celery and carrots and cook for about one more minute. Season with garlic, bay leaves, thyme and salt and pepper to taste. Cook for another minute.
Deglaze the pot with white wine, stirring until nothing is stuck to the pan, then pour in the chicken broth. Simmer for 90 minutes.
Return the chicken breasts to the pan and simmer for an additional 30 minutes. The mixture should reduce considerably by this time so check frequently to see that the chicken is covered. Spoon baste if necessary. The ragout should have a stew like consistency when finished.
