I always start by patting the chicken thighs completely dry, then seasoning generously with salt and pepper. Heat the olive oil in your skillet over medium-high heat, and sear the chicken skin-side down for about 5 minutes until deeply golden. Flip and sear the other side briefly, then set the chicken aside on a plate.
In the same skillet, drop in the chopped bacon and let it render for a couple of minutes until it starts turning crisp. Add the sliced onion and cook until soft and translucent, stirring occasionally so nothing sticks. This step builds the flavor base that carries the whole dish.
Stir in the sauerkraut, grated apple, brown sugar, and caraway seeds, mixing everything together in the pan. Pour in the chicken broth and give it a good stir, scraping up any browned bits from the bottom. Let this simmer for a couple of minutes so the flavors start to combine.
Place the seared chicken thighs skin-side up on top of the sauerkraut mixture, pressing them in slightly so they're partially submerged. This lets the chicken keep cooking through while the skin stays exposed and crisp. Don't fully bury the chicken, or the skin will turn soggy instead of golden.
Transfer the skillet to a 375°F oven and bake uncovered for about 30 to 35 minutes. You're looking for the chicken to reach an internal temperature of 165°F and the skin to look deeply golden and crisp. If it needs a touch more color, a couple of minutes under the broiler works wonders.
Once out of the oven, I like to stir a spoonful of sour cream into the sauerkraut right in the pan for a little creaminess, though this step is completely optional. Let everything rest for five minutes before serving so the juices settle back into the meat. Then plate it up while it's still hot and bubbling.