Preheat oven to 400° F.
Season chicken thighs with salt and pepper. Place chicken thighs skin-side down in a cold cast iron skillet and set on stove over medium-low heat.
Cook on the skillet for 10 minutes. Don't touch the thighs at this point.
After 10 minutes, the chicken thighs should be lightly browned and the skin will be somewhat crispy.
Remove the thighs from the skillet and set aside.
Add sliced pears and carrots to the skillet and cook over medium heat for 3-4 minutes.
Add chicken stock and apple cider vinegar to the skillet and use the liquid to scrape up any bits stuck to the pan.
Return the chicken thighs to the skillet, skin-side up.
Place the skillet in the oven and roast for 15-20 minutes or until the chicken is cooked through. Use a thermometer for doneness. It should reach 165° F in the thickest part of the thigh and the juices should run clear.
Remove skillet from the oven and serve the chicken thighs, pears, and carrots over rice, another grain, or greens.
Spoon a little pan sauce over the chicken before serving.