In a large nonstick skillet over medium heat, heat 1 tablespoon of the oil. Saute the apple until lightly browned, about 5 minutes. Sprinkle with the brown sugar; cook, stirring frequently, until tender, 3-5 minutes longer. Transfer to plate.
On a sheet of wax paper, sprinkle the chicken with the cinnamon, salt, and pepper. In the skillet, heat the remaining 1 tablespoon oil. Saute the chicken until browned, 4-5 minutes on each side. Transfer to another plate.
In the skillet, cook the onion, covered until tender, 6-8 minutes; stir in the cider and vinegar. Reduce the heat and simmer 2 minutes. Return th chicken to th skillet; simmer, spooning the sauce over chicken, until chicken is cooked through and liquid is reduced by half 4-5 minutes.
Return the apples to the skillet; cook until heated through, about 2 minutes. Arrange the noodles on a platter; top the chicken mixture, pouring any remaining juices over chicken.