Remove the moisture from the chicken with paper towels. Heat up a Dutch oven over a medium flame, then pour in 2 Tbl peanut oil. Sear the chicken in oil on both sides. Season the chicken pieces with salt and pepper, then remove it from the pan. Degrease the pan.
Chop the mushrooms, garlic and shallot finely. Melt the butter in the Dutch oven, and add the mushrooms - sauting them over a relatively high flame for a few minutes. Add the chopped shallots, allowing them to sweat for several more minutes. (Mushrooms and shallots sweated down constitutes a duxelles, a French culinary invention.) Deglaze the pan with white wine, and add the demi-glaze, tomatoes, garlic, tarragon and chicken to the pan. Adjust for seasoning. Bring to a boil, then cut to a simmer. Cover tightly and braise in the oven for 30-40 minutes.
Remove the pan from the oven. Serve over rice.