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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 with the onion and garlic for 5 mins until both are lightly browned. Turn over the chicken once and stir the onion regularly.
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 asparagus and cook for 3 mins more. Chop the remaining tarragon.
Stir the crème fraîche and tarragon into the pan with the chicken and heat through, stirring, for a few secs. Serve with the new potatoes.