1. Allow dried mushrooms to soak in hot water for 15 minutes. Drain and preserve the liquid. Chop the mushrooms and keep aside.
2. Heat olive oil and butter in a large frying pan over medium-high flame. Season chicken with salt and pepper. Pan fry for 5 minutes, starting with the skin side down. Flip the breasts over and continue frying for 3-4 minutes. Remove from the pan and set aside.
3. Add onions and fry for 3-4 minutes. Mix in chestnut mushrooms and fry for another 3 minutes. Add garlic and reserved chopped mushrooms and fry for 1 minute.
4. Pour in 100ml mushroom soaking liquid and hot stock along with two-thirds of chopped tarragon. Return browned chicken pieces to the pan. Bring to a boil and then reduce heat to simmer for 10 minutes or until the chicken is cooked through. Ensure there is no pink when cutting into the thickest part of the breast.
5. Stir in crème fraîche and heat through but avoid boiling. Sprinkle the remaining tarragon and serve with green beans and steamed basmati and wild rice.