Cook macaroni according to package instructions. Drain and set aside.
Melt butter in a large Dutch oven over medium heat. Gradually whisk in flour until a thick paste forms. Cook until golden, about 1 minute.
Pour in milk, whisking constantly, until thickened and bubbling, about 5 minutes. Continue to cook and stir until sauce is smooth, about 1 minute more. Reduce heat and season with pepper.
Stir Cheddar and Monterey Jack into the sauce until melted and combined. Stir in hot sauce. Taste cheese sauce to determine if you want more "heat". If so, add more hot sauce.
Add Gorgonzola, chicken, and macaroni; mix well to combine before serving.