In a skillet cook onion in 2 tablespoons butter over moderate heat until softened.
In a 6- to 8-quart heavy kettle melt remaining 6 tablespoons butter over moderately low heat and whisk in flour. Cook roux, whisking constantly, 3 minutes. Stir in onion and gradually add broth and half-and-half, whisking constantly.
Bring mixture to a boil and simmer, stirring occasionally, 5 minutes, or until thickened. Stir in Tabasco, chili powder, cumin, salt, and white pepper.
Add beans, chilies, chicken, and Monterey Jack and cook mixture over moderately low heat, stirring, 20 minutes. Stir sour cream into chili.