Combine the broth, lemon zest and juice, the 2 teaspoons salt, the turmeric and 1/2 teaspoon pepper in a 6-quart Dutch oven or stock pot. Bring to a simmer over medium heat, stirring occasionally.
Reduce the heat to low and add the chicken, carrots and rice. Cover and simmer until the rice is tender, 18 to 20 minutes. Add the kale and chopped dill. Cook just until the kale has wilted, 1 to 2 minutes. Taste for seasoning.
Ladle the soup into shallow bowls and garnish each with a few dill sprigs and more black pepper.