Combine rice, sour cream, and salt in a medium mixing bowl; stir well. Spoon one-third of rice mixture into a buttered 2-quart casserole.
Layer half each of cubed cheese and green chiles on top; repeat layers with rice mixture, cubed cheese, and chiles, ending with remaining rice mixture. Sprinkle shredded cheese over top. Bake at 350° for 30 minutes or until thoroughly heated and cheese melts. Serve hot.