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Season chicken pieces with salt and pepper. In a 10- to 12-inch saute pan, heat 3 tablespoons olive oil over medium-high heat until hot but not smoking. Add chicken pieces skin side down; brown on both sides, about 5 minutes per side. Transfer to a plate; set aside.
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In same pan, combine potatoes, peppers, celery, eggplant, carrots, tomatoes, olives, capers, and chiles; cook until softened, but not browned, about 5 minutes. Season with salt and pepper. Add wine, return chicken to pan, and bring to a boil. Lower heat to simmer, cover; cook until chicken is cooked through, 15 to 20 minutes.
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Stir in mint, parsley, and red pepper flakes. Transfer stew to a large serving dish. Allow to cool to room temperature. Drizzle with olive oil, and serve.