Rub the chicken with the garlic and sprinkle with salt and pepper. Heat the butter with the oil in a heavy skillet over medium heat. Sauté the chicken, about half the pieces at a time, until well browned on both sides, about 6 minutes. Transfer to a plate.
Pour off all but 1 tablespoon drippings from the skillet. Add the shallot and cook over medium low heat scraping the bottom and sides of the pan with a wooden spoon, 2 minutes. Return the chicken pieces to the skillet. Sprinkle the vinegar over the chicken and stir gently until the juices have almost evaporated. Stir the tomatoes around the chicken pieces. Pour the stock over the chicken and heat to boiling. Reduce the heat and simmer, covered, 30 minutes.
Rinse the quinoa under cold running water. Drain. Stir the quinoa into the juices around the chicken. Continue to cook, covered, until the quinoa is tender, about 15 minutes. Sprinkle with the tarragon and parsley. Serves 4