In a deep sided 12 inch skillet, heat the oil with 1 tablespoon of butter over high heat. Season the chicken thighs well with salt and pepper. When the fats are hot but not smoking, add the chicken and cook on both sides until the skin turns an even golden brown, and the chicken is cooked to the desired doneness, about 12 minutes on each side.
Carefully regulate the heat to avoid scorching the skin. If the pan is not big enough, prepare the chicken in several batches.
Transfer the chicken to a serving platter, cover loosely with aluminum foil. Keep warm.
Pour off the fat in the skillet. Return the skillet to medium high heat and add the wine. Deglaze the pan, scraping up any bits that may have cling to the skillet. Add the shallots and tomatoes and cook for several minutes.
Raise the heat to high and slowly add the vinegar. Cook for another 2 to 3 minutes. whisk in the remaining 2 tablespoons of butter, cook for 1 minute, return the chicken to the skillet and coat well with the sauce. Cover and cook over medium heat until the chicken absorbs some of the sauce. Sprinkle with tarragon and turn the chicken pieces to coat. Serve immediately.