In a large skillet, heat half of the oil and half of the butter over medium heat until bubbly. Add apples; saute for 5 to 8 minutes or until golden. Transfer to a platter; set aside.
Increase heat to medium-high. Add remaining oil and butter to skillet. Season chicken with salt and pepper. Add half of chicken to skillet; cook about 5 minutes per side or until golden brown. Transfer chicken to platter with apples. Repeat with remaining chicken. Wipe out skillet. Return all chicken to skillet.
In a small bowl, whisk together cider, brandy, and cinnamon; add to skillet. Bring to boiling; reduce heat. Cover and simmer for 25 minutes, turning chicken halfway through cooking. Add apples to skillet; cover and cook about 20 minutes or until apples are tender and chicken is no longer pink (170 degrees F in breasts, 180 degrees F in thighs and drumsticks). Transfer chicken and apples to a serving platter; keep warm.
Bring liquid in skillet to a boil. Boil gently until it barely coats bottom of skillet. Remove from heat; whisk in sour cream until well blended. Return chicken and apples to skillet. Cover and simmer about 5 minutes or until heated through.