Step 1

Preheat broiler with rack 6 inches from heating element. Season polenta and chicken with salt and pepper. Heat a large ovenproof skillet (preferably cast iron) over medium-high; swirl in 2 tablespoons oil. Add polenta and cook, flipping once, until golden and crisp on edges, about 4 minutes. Transfer to a plate.

Step 2

Add chicken to skillet; cook until browned on edges and cooked through, about 2 minutes a side. Transfer to plate. Add 1 tablespoon oil, olives, capers, and garlic to skillet; cook until fragrant, 30 seconds.

Step 3

Stir marinara into skillet; bring to a boil. Remove from heat; nestle in chicken and polenta, shingling them and spooning some sauce over top. Sprinkle with cheese; broil until bubbly, 4 to 5 minutes. Top with parsley; serve.