Preheat the oven to 170°C. Put the chicken in a 3-quart glass or ceramic baking dish and sprinkle with salt and pepper. Bake until just cooked through, 25 to 30 minutes.
Meanwhile, heat the oil in a large saucepan over medium heat. Add the garlic, onions, peppers and 1/4 teaspoon salt. Cook, stirring occasionally, until the vegetables are tender, about 15 minutes. If the mixture becomes too dry, add a tablespoon or two of water. Stir in the sweet and hot paprika and cook for 1 minute; add the tomato paste and cook another minute, stirring. Add the chicken broth and 2 cups water. Bring to a boil, and then reduce the heat to maintain a steady simmer. Simmer until thickened, about 5 minutes.
Transfer the chicken to a plate. Spread the rice in the bottom of the casserole dish and top with the chicken and its accumulated juices. Pour the sauce over the whole mixture. Bake until the casserole is heated through and the top is browned lightly, 40 minutes. Top with the chopped parsley and serve with a dollop of sour cream.