Cook the potatoes in a large pan of boiling water for 8-10 mins until tender, then drain and keep warm in the pan. Season the chicken with ground black pepper. Heat the oil in a large non-stick frying pan. Gently fry the chicken for 5 mins. Turn over the chicken.
Pour over the stock, add 2 sprigs of tarragon and bring to a gentle simmer. Cook for 5 mins, then turn the chicken, add the green beans and cook for 3 mins more. Chop the remaining tarragon.
Stir the lactose free cream, garlic infused oil and tarragon into the pan with the chicken and heat through, stirring, for a few secs. Serve with the new potatoes.