In a large bowl, cover sauerkraut with water. Heat a large Dutch oven or other heavy pot over medium-high. Season chicken with salt and pepper. Add to pot, skin side down, and cook, turning until browned on all sides, 8 minutes. Transfer chicken to a plate. Add kielbasa, cut side down, to pot and cook until browned on both sides, about 4 minutes, flipping once. Add carrots, onion, and 1/2 cup water; cook, stirring and scraping up browned bits with a wooden spoon, until water is evaporated and onion is softened, 6 to 8 minutes. Add wine and bring to a boil.