Sprinkle chicken breasts with salt and pepper. Season the flour with salt and pepper; dredge the chicken breasts in the mixture and shake off excess. Heat the oil in a skillet over medium-high heat. Cook the chicken breasts until nicely browned on one side, about 3 minutes. Add the garlic cloves. Turn the chicken pieces and scatter the mushrooms over them; shake skillet, cook 3 minutes and add vinegar, broth, bay leaf and thyme.
Cover tightly and cook over medium-low heat for 10 minutes, turning pieces occasionally. Transfer chicken to warm platter. Cook sauce with mushrooms, uncovered, over medium-high heat for about 7 minutes. Swirl in the butter. Discard bay leaf. Pour sauce over chicken and serve.