In a 5-quart Dutch oven or heavy pot, heat 2 tablespoons oil over medium-high. Season chicken with salt and pepper. Working in two batches, sear chicken, meaty side down, until browned, 6 to 8 minutes; transfer to a plate (chicken will cook more in step 2).
Add mushrooms to pot; cook, stirring occasionally, until browned, 2 to 3 minutes. Add flour, and cook, stirring, 1 minute. Add tomatoes (with their juice), wine, onions, garlic, olives, and chicken (with any juices). Bring to a boil; reduce to a simmer, and cook until chicken is cooked through, 15 to 20 minutes. Season stew with salt and pepper.
While stew is cooking, heat broiler. On a rimmed baking sheet, brush both sides of polenta slices with remaining oil; season with salt and pepper. Broil, without turning, until deep golden brown, 10 to 15 minutes. Serve chicken cacciatore over polenta.
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