Melt 1/4 cup of the butter in a large skillet over medium high heat. Brown chicken in butter quickly, and remove to a 9x13 inch baking dish.
Add remaining 1/4 cup butter to skillet and brown the green onion and mushrooms with the garlic and tarragon. Pour this saute mixture over chicken breasts.
Preheat oven to 350 degrees F (175 degrees C).
Heat the cream, cheese and amaretto in the skillet, whisking rapidly. Stir in capers, then pour sauce over chicken, green onions and mushrooms.
Bake in the preheated oven for 40 minutes, or until chicken is cooked through and no longer pink inside.
