In a large, heavy Dutch oven or deep skillet, heat the oil over high heat until very hot but not smoking. Season the chicken on both sides with salt and pepper and brown on both sides in the olive oil, about 4 to 5 minutes per side. Remove the chicken to a bowl or platter and set aside.
Add the onion, garlic, bell pepper, and crushed red pepper to the drippings in the skillet and saute until the vegetables are tender and beginning to caramelize around the edges, about 5 to 7 minutes, stirring frequently. Add the wine and cook until the liquid is almost evaporated, 3 to 5 minutes. Dust the vegetables in the skillet with the flour, mix well and cook for 2 to 3 minutes. Add the tomatoes and chicken stock and cook until the mixture is slightly thickened, about 5 minutes. Return the chicken pieces to the Dutch oven and add the olives.
When mixture returns to a boil, cover the Dutch oven and reduce the heat so that the mixture just simmers. Cook 30 to 45 minutes, or until the chicken is very tender. While the chicken is cooking, make the polenta.
Polenta: Heat the water to boiling in a large saucepan. Add the polenta in a stream, while whisking. Cook, stirring constantly until the polenta is thick and smooth, about 25 to 30 minutes. Stir in thyme, cheese, and butter and season with salt and pepper.
Gently transfer the chicken to an ovenproof bowl or platter and cover to keep warm. If the sauce seems thin, increase the heat and reduce the sauce to the appropriate thickness. Taste, adjust seasoning if necessary, and serve the sauce ladled over the chicken.
Spoon the polenta onto a platter and top with the chicken and sauce.
Yield: 6 to 8 servings
*Green olives from Cerignola, typically labeled Cerignola Olives, are beautiful green olives with a subtle, fresh olive flavor, about twice the size of most olives. They were the inspiration for this dish, but good results can be achieved by using the more commonly available Spanish