Sprinkle chicken with 1/2 tsp salt and 1/4 tsp pepper. Heat a large pot over medium-high heat. Add 1 tablespoon oil to pan; swirl to coat. Add half of chicken to pan, saute 5-6 minutes until chicken is browned. Remove chicken from pan, repeat procedure with remaining chicken.
Reduce heat to medium; add remaining 1 tablespoon oil to pan. Add onion, garlic, red pepper, ginger and cinnamon. Cook 2 minutes, stirring occasionally. Add squash, cook 2 minutes more. Sprinkle vegetables with flour and cook 1 minute, stirring occasionally. Stir in cider and chicken stock, scraping pan to loosen browned bits. Stir in chicken, remaining salt and pepper. Bring to a simmer. Reduce heat, partially cover, simmer 20 minutes, stir in apple. Cook another 10 minutes or until apple is tender.