Heat half the oil in a skillet over moderate heat.
Season the chicken with salt and pepper and brown on both sides.
Transfer to a greased baking dish.
In the same skillet, heat the remaining oil and saute the scallions, garlic, and mushrooms for 5 minutes.
Add to the baking dish. In the same skillet add the stock, wine, tarragon, salt, and pepper, and bring to a boil, stirring constantly.
Remove from the heat.
Mix the flour and sour cream in a small bowl and whisk into the liquid until smooth.
Pour over the chicken and bake in a preheated 350F oven until the chicken is cooked through, about 35 minutes.
Serve with the mushrooms spooned over the chicken and garnished with a tarragon sprig if desired on a bed of hot bed of white rice or new potatoes and seasonal greens.