Sprinkle chicken with salt and pepper; dust with flour. Heat oil in heavy large skillet over medium-high heat. Add chicken; sauté until brown, about 4 minutes per side. Transfer to plate. Add mushrooms, shallots and herbs to skillet. Sauté until mushrooms are cooked through and juices are reduced to glaze, about 12 minutes.
Add broth and wine to skillet. Boil until reduced by half, about 8 minutes. Return chicken to skillet. Simmer until chicken is cooked through and liquid thickens to sauce consistency, about 6 minutes. Season with salt and pepper. Transfer chicken and sauce to plates.
