Preheat the grill. Brush peppers with oil and arrange on a baking tray. Grill peppers 5 minutes, turning occasionally, until scorched on all sides. Remove from heat, cool slightly, and peel.
Preheat the oven to 180 C / Gas 4.
In a bowl, mix the shredded chicken, 1/2 of the cheese, and 1/3 of the enchilada sauce. Cut a slit in each roasted chilli, and stuff each with about 1 tablespoon of the chicken mixture. Arrange stuffed chillies in a single layer in a large baking dish. Cover with the remaining enchilada sauce.
Bake 35 minutes in the preheated oven, until bubbly. Sprinkle with remaining cheese, and continue baking 5 minutes, or until cheese is melted. Garnish with olives and soured cream to serve.