Heat oil in a Dutch oven over medium-high heat. Add the 1 cup chopped onion, the sweet peppers, and garlic; cook for 3 minutes. Add chicken. Cook and stir for 3 minutes or until chicken is browned. Drain off fat.
Add undrained tomatoes, beans, the water, vinegar, coffee, chili powder, cocoa powder, cumin, and cayenne pepper. Bring to boiling; reduce heat. Simmer, covered, for 30 minutes, stirring occasionally.
Serve with cheddar cheese and finely chopped onion, if desired. Makes 6 servings.