1. Cut your chicken breast into smallish pieces, I like to cut mine into fingers about 1/2 wide and 3 long - you can also dice it into cubes if you wish.
2. Heat the butter and oil until sizzling but not brown, add the chopped tarragon and chicken pieces immediately (skin side down if using chicken with skin) and cook for 3 to 4 minutes until the chicken is sticky and a nice caramel colour; the butter will have browned by now, but that is fine as long as it does not burn. Turn the chicken over and cook another 1 to 2 minutes.
3. Add some crème fraiche to your own requirements - I use about 2 tablespoons, but you can add more later. Allow to bubble for about 2 minutes and then add some lemon juice to taste. Season with salt and pepper and adjust the consistency if you want it creamier.
4. Serve with fresh tarragon leaves scattered over the top and a side salad with French dressing. Bon appétit!