In a pestle and mortar, pound the tarragon with couple pinches of salt & black pepper, 1tbsp oil and 3 cloves of garlic into a paste.
Make a little pocket under the skin of each of the breasts and stuff 1 tsp of the tarragon mixture into it.spread the rest over the meat.
Place the chicken breasts into a plastic food bag with the wine and remaining garlic, thickly sliced, and expel as much air as you can from the bag. Marinate in the fridge for about 1 hour then remove the chicken and pat dry on kitchen paper. Strain the marinade and reserve the garlic but discard the wine.
Preheat the oven to 180°C/gas4.
In a large flameproof casserole dish, heat the remaining olive oil over a medium heat and fry the chicken skin side down until golden, do this in batches if need be. Remove and set aside.
Allow the pan to cool down, then place the herbs and reserved garlic in the dish.Add the chicken skin side up and add the stock.
Cover with greaseproof paper. Place in the oven, then immediately turn the heat down to 140°C/gas 1. Cook for 1 hour 30 minutes, or until the chicken is cooked through and there is no pink meat. remove the herb sprigs and serve.