Cook the rice: In a medium saucepan, bring the chicken broth to a boil. Add rice, reduce heat, cover, and simmer until the rice is tender and the liquid is absorbed, about 15-20 minutes.
Sauté onions and garlic: While the rice cooks, heat olive oil in a skillet over medium heat. Add onion and garlic, cooking until the onion is translucent.
Combine ingredients: In a large mixing bowl, combine the cooked rice, cooked chicken, sautéed onion and garlic, heavy cream, and sour cream. Season with salt and pepper to taste.
Assemble the casserole: Transfer the mixture to a greased baking dish. Sprinkle with cheddar and Parmesan cheeses.
Bake: Place in the oven and bake for 25-30 minutes, or until the cheese is bubbly and golden brown.
Garnish and serve: Sprinkle chopped parsley over the top before serving.