Cut chicken breasts into strips and season with salt and pepper. Place on a baking sheet coated with non-stick spray and bake at 375 until just done, about 15 minutes. Chop strips into cubes.
In a skillet cook onion and garlic in 2 tablespoons butter until softened but not brown.
In a 6- to 8-quart heavy pot melt remaining 6 tablespoons butter over moderately low heat and whisk in flour. Cook roux, whisking frequently, 3 minutes.
Stir in onion and gradually add broth and half-and-half, whisking constantly. Bring mixture to a boil and then reduce to a simmer, stirring occasionally, until thickened, about five minutes.
Stir in Tabasco or Cholula, chili powder, cumin, and black pepper. Add beans, chilies, chicken, and Monterey Jack and cook mixture over moderately low heat, stirring as needed, about 20 minutes. Salt to taste and add more Cholula if it needs more kick.
Serve with tortilla chips and Cholula.