MICROWAVE potatoes and water in covered microwavable dish on HIGH 10 minutes, stirring after 5 minutes; drain. (Potatoes should be not quite done.)
HEAT oil in large nonstick skillet on medium heat. Add chicken; cover. Cook 5 minutes on each side or until chicken is cooked through. Remove chicken from skillet; set aside.
ADD potatoes to skillet; cook 5 minutes until lightly browned, stirring occasionally. Reduce heat to low. Stir in 1/2 cup of the barbecue sauce; top with chicken. Pour remaining 1/4 cup barbecue sauce over chicken; sprinkle with cheese. Cover. Cook 5 minutes or until cheese is melted.