Trim the chicken skin so that it just covers the thighs, removing any fat with it.
Peel and thickly slice the carrots. Peel, halve and slice the onion. Place the carrot in a 2 litre/31⁄2pt capacity, lidded pan with the onion, thyme, parsley, 3 sprigs of tarragon, wine, peppercorns, bay leaf and 1 tsp salt.
Lay the chicken, skin-side uppermost, on top and cover with 1 litre/13⁄4pt cold water. Bring the liquid to the boil, skimming away any scum that forms and immediately reduce the heat. Cook with hardly a tremble to the water for 40 minutes.
Lift the chicken on to a plate and strain the stock into a sauté or other wide-based pan. Return the chicken to the original pan, add about 300ml/1⁄2pt of the hot stock, cover and leave to rest and keep warm while you complete the sauce.
Boil the stock until thick and syrupy and reduced to about 200ml/7fl oz. Add the crème fraîche or cream, stirring until thoroughly mixed, then simmer briskly for a few minutes until thick and slightly reduced. Stir in 2tsp chopped tarragon leaves, taste and adjust the seasoning with a squeeze of lemon juice, simmer for 1 minute and turn off the heat.
Remove the skin from the chicken thighs, arrange them in a serving dish and pour the sauce over them.
Lindsey Bareham's website is: www.lindseybareham.com