Preheat oven to 450 degrees.
Wash chicken, inside and out, with cold running water. Pat dry. Season inside and out with salt and pepper.
Place the tarragon sprigs and halved onion in the cavity. Tuck wings tips under.
Tie the legs together with butcher's twine. Heat the oil in a medium nonstick roasting pan.
Place the chicken, on its side, in the pan. Roast, basting every 10 minutes for 20 minutes.
Turn the chicken on its other side, and add the water. Reduce the oven heat to 400 degrees.
Roast, basting every ten minutes, for 20 minutes. Turn the chicken on its back.
Add carrots, onions, garlic, parsley , thyme and bay leaf. Continue roasting for 10 more minutes, or until an instant-read thermometer inserted in the center of the breast registers 170 degrees.
Remove the chicken form the oven, and lift onto a platter. Cover loosely with foil.
Strain the vegetables and fat in a bowl. Discard fat and herbs. Return vegetables to the pan.
Add wine and stock to roasting pan. Heat to deglaze and simmer 5 minutes.
Strain into a saucepan and stir in the chopped tarragon. Season with salt and pepper.
Cut the breasts and legs from the chicken. Slice each breast across in two pieces. Separate the drumsticks form the thighs. Serve with the hot sauce.
Serve with rice, potatoes or noodles