Combine flour, thyme,salt, and pepper in a shallow bowl.
in a skillet, heat 2 tablespoons oil over medium high heat. Add mushrooms and cook for 10 minutes. Transfer the mushrooms to a small bowl and set aside.
Heat remaining 2 tablespoons oil in the skillet. Dip chicken in flour mixture. Shake off excess flour and place chicken in hot oi. Do not crowd chicken or it will steam instead of brown. Cook for 5 minutes on each side. Transfer to a platter and cover with foil to keep warm.
Once all of the chicken has been cooked, add wine to the skillet, stirring up all of the browned bits and pieces. Increase heat to high and continue cooking for 2 minutes. Stir in brith and cook for 3 minutes more or until sauce thickens. Return mushrooms to pan and heat through.