Preheat oven to 425 degrees F. Lay sweet potatoes cut side up on a large baking sheet. Roast until tender, about 35 minutes, depending on size of your potatoes. Place chicken breasts in oven at same time and bake for 25-35 minutes.
In a saucepan set to medium-low, stir together chicken and BBQ sauce. Heat until warm, 5-10 minutes.
Top each potato with scoopfuls of chicken. Spoon over additional BBQ sauce and sprinkle with chopped parsley or sliced green onions, if desired.