Preheat oven to 350°F. Season chicken with salt and pepper. Heat olive oil in heavy large Dutch oven over medium-high heat. Working in batches, add chicken to pot and sauté until brown, about 8 minutes per batch. Transfer chicken to bowl. Add onion to pot and sauté until golden, about 5 minutes. Remove pot from heat. Spread 1/3 of carrots over onion, then 1/3 of rice and 1/3 of prunes. Arrange half of chicken atop prunes. Season with paprika, salt and pepper. Repeat layering with 1/3 each of carrots, rice and prunes. Top with remaining chicken; season with paprika, salt and pepper. Layer remaining carrots, rice and prunes over. Pour stock over. Cover pot and place in oven. Bake until chicken and rice are cooked through, about 1 hour.