HEAT 1 Tbsp. of the oil in large skillet on medium-high heat. Add chicken; cover. Cook 10 min. on each side or until cooked through (170ºF). Remove chicken from skillet to serving platter, reserving drippings in skillet; cover chicken to keep warm.
ADD remaining 1 Tbsp. oil, the mushrooms and onions to skillet; cook and stir 5 min. or until onions are crisp-tender. Reduce heat to low.
STIR in sour cream and barbecue sauce until well blended; cook 2 min. or until heated through, stirring occasionally. Spoon over the chicken; sprinkle with parsley.