Heat water and apples in a skillet over medium-high heat, cook until tender, about 3 to 4 minutes. In a small bowl, mix the cooked apple, cranberries, shallots and a splash of the chicken stock and set aside.
Cut a deep horizontal pocket in the side of each chicken breast. Make the pocket as large as you can without piercing the top or bottom of the breast. Place ¼ of the apple mixture in the pocket of each chicken breast. Secure the pocket with toothpicks, threading along the side to close.
Heat the 1½ tablespoons oil in a heavy oven-proof skillet until it just begins to lightly smoke (oil should shimmer at the ‘ready’ temperature). Sear each side of the chicken until golden brown. Add the vinegar and chicken stock and bring to a boil. Lower the heat and gently simmer the chicken for 4–6 minutes, until cooked through, turning breasts over in the stock midway through cooking. Remove the chicken breasts from the skillet and keep warm. Continue to cook the sauce until it is reduced to a thick syrup. Taste the sauce and season with salt and pepper. Spoon the sauce over each chicken breast to serve.