Peel, core and chop apple. Melt 2 tablespoon butter in a heavy medium skillet over medium heat. Add apple, honey and lemon juice. Sauté until apple is just tender and golden, about 4 minutes.
Place flour in a bowl. Season with salt and pepper. Dredge chicken in flour. Melt 2 tablespoon butter in heavy large skillet over medium heat. Add chicken and cook until golden and cooked through, about 4 minutes per side. Transfer to plate and tent with foil.
Add chicken stock, apple and cranberry juices, applejack and cinnamon stick to same skillet and bring to a boil, scraping up any brown bits. Simmer until reduced to 2/3 cup, about 15 minutes. Stir in apple mixture and remaining 3 tablespoon butter. Season with salt and pepper. Discard cinnamon stick. Ladle sauce over chicken. Sprinkle with chives and serve.