Preheat oven to 350 degrees. Spread the melted butter in a 9x13 baking dish.
Prepare spaghetti according to package directions to al dente. Drain, leaving a small amount of pasta water in the pot. Return the pasta to the pot.
Add the cheese sauce, cream of chicken soup, and chicken broth to the pasta. Stir until smooth and creamy. Add the spices and stir.
Fold in the cooked chicken, tomatoes, green chiles, and black olives.
Transfer the mixture to the buttered baking dish. Bake uncovered for 30 minutes until hot and bubbly.