Heat 2 tablespoons of the butter in a heavy frypan and add the chicken, skin side down. Cook for five minutes until skin is nicely browned. Turn the pieces and reduce the heat to medium. Cook until even brown all over, about 15 minutes, turning as necessary.
Place the chicken on a warm plate and cover with foil. Keep warm.
To the drippings in the frypan add the mushrooms, salt and pepper to taste and cook, stirring, until the mushrooms start to brown, about 2 minutes. Add the onion, shallots, bay leaf, garlic and thyme.
Sprinkle with flour and add the chicken stock and wine, stirring until smooth. Simmer about 10 minutes.
Stir in the remaining 2 tablespoons butter, then add the chicken and any juices that have accumulated to reheat. Serve!