First things first! Make sure your pasta is cooking while you prepare the rest of this meal. Then, in a large nonstick skillet over medium heat, heat 1 tablespoon of the oil. Sauté the apple until lightly browned, about 5 minutes. Sprinkle with brown sugar and cook and additional 3 to 5 minutes, just until tender. Remove apples from the pan to a bowl.
Place the chicken on a plate and sprinkle with cinnamon, salt and pepper (on one side is fine). Heat the remaining tablespoon of oil and cook the chicken 4 to 5 minutes on each side, just until browned. Remove the chicken from the pan and onto a plate.
Add the onion to the pan and cook (covered) over medium heat 6 to 8 minutes, or until very tender (stir once in a while). Add the cider and vinegar, then reduce heat and simmer 2 minutes. Return the chicken to the skillet and continue to simmer until the chicken is cooked through and the liquid is slightly reduced, 4 to 5 minutes (I like to cover the pan here so the chicken can cook more quickly).
Return the apples to the skillet and heat through. For each serving, place ½ cup noodles on a plate and top with one piece of chicken and ¼ cup sauce.