Preheat oven to 350 degrees. Season chicken breasts with salt and black pepper.
Heat 2 tablespoons olive oil over medium-high heat in a Dutch oven.
Place chicken breasts skin side down in the hot oil and brown 4-5 minutes or until golden. Turn and brown the other side approximately 4-5 minutes. Transfer to a plate.
Heat remaining 1 tablespoon olive oil in the Dutch oven and add the onion.
Reduce heat to medium and cook onion 3-4 minutes or until softened.
Add garlic and cook 30 seconds or until fragrant. Stir in tomatoes and cook 1 minute.
Add the wine and bring to a boil, scraping up any browned bits. Add the chicken broth, oregano and thyme and return to a boil.
Place chicken skin side down in the pot, cover tightly and place in the oven. Cook 1 hour, turning once or until chicken is thoroughly cooked and tender. Transfer Dutch oven to the stovetop.
Combine 1 tablespoon butter with flour. Add to pot with chicken and bring to a simmer to thicken.
Heat remaining 1 tablespoon butter over medium-high heat in a skillet or saute pan.
Add the mushrooms and cook 4-5 minutes or until browned. Transfer to pot with chicken, stir in chopped fresh basil, adjust seasoning with salt and black pepper and serve.
