Heat half the oil and half the butter in large skillet over medium heat until bubbly. Add apples; sauté until lightly golden, 5 to 8 minutes. Remove to platter and 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 5 minutes or until golden brown; cook other side. Remove chicken to platter with apples. Cook remaining chicken. Discard drippings from skillet. Return reserved chicken to skillet.
Whisk together cider, brandy and cinnamon in small bowl. Pour into skillet. Cover; simmer 25 minutes, turning chicken over halfway through. Add apples to skillet; cook 20 minutes. Remove chicken and apples from skillet to platter. Boil liquid in skillet until it barely coats bottom. Turn off heat, whisk sour cream into cider mixture in skillet until well blended.
Return chicken and apples to skillet. Cover; simmer 5 minutes until chicken and apples are tender.