Preheat the oven to gas 6, 200ºC, fan 180ºC. Put the chicken in a shallow casserole dish or roasting tin. Drizzle with 1 tablespoon of the oil, stuff the cavity with half the tarragon and season. Roast in the oven for about 1½ hours, until the juices run clear when you pierce the flesh of the thigh with a skewer.
Meanwhile, put the rosemary and potatoes in a roasting tin with the remaining oil and toss well. Season, then put in the oven 50 minutes into the chicken cooking time and roast for 40 minutes (if the potatoes are ready before the chicken is quite cooked, keep the potatoes somewhere warm until ready to serve).
When the chicken is cooked through and the juices run clear when a skewer is inserted, remove the chicken from the oven, then take it out of the tin and set aside, loosely tented with foil to rest. To make the tarragon cream sauce, put the pan of meat juices on the hob over a medium heat and add about 100ml (3½fl oz) of water or stock and stir well, scraping up any sticky bits on the bottom of the pan. Add the shallots and cook for 5-10 minutes until softened but not crispy. Chop the remaining tarragon, turn the heat down and add to the sauce, then add the cream. Stir well and bring just to the boil, then season to taste. Slice the chicken and serve with the potatoes and cream sauce.
For top tips on protecting you and your family when preparing raw meat and poultry, visit Food Safety in the Home and view the full Food safety at home video.