Pat the chicken dry with paper towels, season on all sides with salt and pepper. Brown chicken or set aside. If browning chicken, heat olive oil in large skillet, brown and remove. Otherwise, set the chicken aside.
Heat olive oil in skillet to medium heat. Add leek, shallot, garlic and thyme. Cook until tender, about 5 minutes.
Add cider/sherry and tarragon, stir.
Stovetop method: Return chicken to the pan. Cover and cook over medium heat for 25 minutes (or until chicken reaches 165⁰ F). Uncover and increase heat to high. Reduce the liquid and cook until apples start to caramelize, about 3-5 minutes. Sprinkle with parsley
Oven or slow cooker method: Preheat oven to 400⁰ F. Put apple mixture in casserole pan and put chicken on top. If the chicken is skinless, cover dish while baking. Remove from oven when chicken reaches 165⁰ F. Or put apple mixture in slow cooker, add chicken, cover and cook on high for 4-5 hours.