Preheat the oven to 180C/350F/Gas 4.
Place the flour into a bowl and season with salt and freshly ground pepper. Dredge the chicken in the flour, shaking off any excess.
Heat a large, deep frying pan and add the oil. Fry the chicken pieces skin-side down for 1-2 minutes until golden-brown, turn over and brown on the other side. Remove the chicken from the pans and set aside.
Add a little more oil if the pans are dry then add the mushrooms and fry for 2-3 minutes. Add the onion and cook for a further five minutes.
Place the chicken back in the pans and add the stock, tomato purée, whole tarragon sprigs and tomatoes. Bring to the boil and transfer the chicken to ovenproof dishes. Cover with aluminium foil and place in the oven for 45 minutes, or until the chicken is cooked through.
Adjust the seasoning if necessary then add the parsley and the chopped tarragon.