1. In a heavy saucepan, bring broth to a boil over medium heat. In a mixing bowl, whisk polenta into cold water until smooth and free of lumps. Slowly whisk dissolved polenta into boiling broth. Reduce heat to medium-low and simmer, stirring almost constantly, until mixture is very thick and pulls away from side of pan, 12 to 15 minutes. Stir in butter, 1/4 cup of cheese, pepper, and salt. Scrape polenta into a buttered 10-inch pie plate. Let cool to room temperature. Sprinkle remaining 2 tablespoons cheese over top.
2. Preheat oven to 350°F. Place chicken in a 2- or 2 1/2-quart baking dish. Pour marinara sauce and wine over chicken. Cover with foil and bake until chicken is cooked through, about 35 minutes.
3. After chicken has been in oven about 15 minutes, place polenta in same oven on upper rack. Bake, uncovered, until lightly flecked with brown and heated through, about 20 minutes.
4. To serve, cut polenta into 6 wedges. Serve each wedge alongside chicken, with sauce spooned over both.