Season the chicken breasts with salt and pepper. Heat olive oil in a large pan over medium-high heat. Sear the chicken until golden on both sides. Set aside.
Reduce the heat to medium. Add the butter to the same pan, then stir in the sliced onion, mushrooms, and garlic. Sauté for about 10 minutes.
Pour in white wine and let it reduce for 2 minutes. Stir in tomato paste, diced tomatoes, chicken stock, tarragon, thyme, and bay leaf. Return the chicken to the pan, cover, and simmer for 20 minutes.