Sprinkle the chicken with salt and pepper. Heat the oil and butter in a heavy-bottom skillet. Add the chicken breasts and sauté over medium¬-high heat, turning the pieces often until lightly browned, about 5 minutes.
Add the shallots and garlic around the chicken. Cook briefly; add the tarragon, tomatoes, vinegar, capers, wine and tomato paste. Stir to dissolve the brown particles adhering to the bottom of the skillet.
Blend well, bring to a boil, and then cover and simmer for 9 minutes. Sprinkle with parsley and serve.