Pat the cleaned chicken dry, and then season the pieces with salt and pepper. In a 12 to 14-inch saute pan, heat 3 tablespoons olive oil until hot but not smoking. Carefully add the chicken pieces and brown on both sides, about 5 minutes per side. Remove chicken from the pan and set aside.
In the pan with the chicken drippings add potatoes, peppers, celery, eggplant, carrot, capers, olives, tomatoes and whole chiles. Toss together. Add the wine and chicken, season with salt and pepper and bring to a boil. Cover, lower the heat to a simmer and cook for about 15 minutes until chicken is cooked through. Remove from the heat and stir in chopped mint, parsley and a pinch of chili flakes.
Transfer the cooked stew to a serving dish and allow to cool to room temperature before serving. Drizzle with extra-virgin olive oil and serve.