Leaving the skins on both the chicken and apple makes all the difference.
4 chicken breasts
2 heirloom apples (a nice tart one such as a Golden Russet, Newtown Pippin, Northern Spy or Winesap)
1/2 cup of calvados
2 cups of apple cider
1 cup of chicken stock
2 tablespoons of butter
2 onions, sliced
1 clove of garlic, minced
1 teaspoon of fresh thyme leaves
2 teaspoons of corn starch dissolved in 1 tablespoon of cold water
1/4 cup of crème fraîche
Make sure the chicken is dry by blotting with a paper towel.
In a pot that you can eventually cover, heat butter over medium-high heat. Once hot, stick in the chicken skin side down and cook for 5 minutes without fidgeting with it. Then flip and cook another 3 minutes.
Remove the chicken and in the same pan, add the onion, garlic, salt and pepper. Cook for 2 minutes, then add the calvados, scrape up the brown bits stuck to the bottom and reduce until almost no liquid is left. Then, add the apple cider, chicken stock and thyme, bring to a boil and put the chicken breasts along with any accumulated juices back in the pan. If the chicken isn't completely covered in liquid, add another cup of apple cider, stock or water. Cover the pot and simmer on low for 25 minutes, flipping once, until the chicken is cooked through (internal temperature of 165ºF).
Remove chicken and add the crème fraîche along with the corn starch dissolved in water. Cook on medium for about 7 minutes to reduce the sauce until it is nice and thick. While the sauce is reducing, core, peel and slice the apple, then toss the pieces into the sauce and remove from heat. Stir well and pour over chicken.