Preheat the oven broiler. Brush peppers with oil and arrange on a baking sheet. Broil peppers 5 minutes, turning occasionally, until scorched on all sides. Remove from heat, cool slightly, and peel. Reduce oven temperature to 350 degrees F (175 degrees C).
In a bowl, mix the shredded chicken, 2 cups cheese, and 1 cup enchilada sauce. Cut a slit in each roasted chile pepper, and stuff each with about 1 tablespoon of the chicken mixture. Arrange stuffed chiles in a single layer in a large baking dish. Cover with the remaining enchilada sauce.
Bake 35 minutes in the 350 degrees F (175 degrees C) oven, until bubbly. Sprinkle with remaining cheese, and continue baking 5 minutes, or until cheese is melted. Garnish with olives and sour cream to serve.
