Preheat oven to 400°.
To prepare chard, remove stems and center ribs. Discard stems and chop ribs; coarsely chop leaves. Heat a large nonstick skillet coated with cooking spray over medium heat. Add garlic; sauté 30 seconds. Add ribs and 2 tablespoons water; cover and cook 5 minutes. Add the leaves; cover and cook 5 minutes or until wilted.
To prepare polenta, place 1 3/4 cups water, salt, and broth into a large saucepan. Gradually add the cornmeal, stirring constantly with a whisk. Bring to a boil; reduce heat to medium, and cook 8 minutes, stirring constantly. Add cheeses, stirring constantly with a whisk. Spoon half the polenta into a 2-quart baking dish coated with cooking spray, spreading evenly. Top with the chard mixture. Spoon sour cream over chard, spreading evenly. Quickly add remaining polenta, spreading evenly.
Bake at 400° for 20 minutes. Let stand 5 minutes.