Season the chicken all over with 1/4 teaspoon of the salt and 1/4 teaspoon of the pepper. In a large sauté pan or Dutch oven over medium-high heat, add the oil. Brown the chicken well on both sides; remove the chicken to a platter. Pour off all but 2 tablespoons of fat from the pan; reduce the heat to medium.
Stir in the onion and the remaining 1/4 teaspoon of salt and 1/4 teaspoon of pepper and cook, stirring occasionally until the onion is soft, about 5 minutes. Stir in the garlic, sage and apple and cook, stirring occasionally, for 2 minutes. Stir in the vinegar, scraping up any brown bits from the bottom of the pan. Stir in the broth, sauerkraut and apple butter. Bring to a boil, partially cover the pan, reduce the heat, and simmer until the chicken is cooked through and tender, about 40 minutes.