Bring a large pot of lightly salted water to a boil. Cook macaroni in the boiling water, stirring occasionally until tender yet firm to the bite, about 8 minutes. Drain.
Cut wings and legs off rotisserie chicken. Remove skin and bones from wings and legs; chop or shred dark meat into bite-sized pieces.
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 to the desired level of spiciness.
Add Gorgonzola, chicken, and macaroni; mix well to combine.
Serve hot and enjoy!
