Cook turkey, onion, and green pepper in a large soup pot or Dutch oven over medium heat until turkey is no longer pink, about 10 minutes, stirring often; rain excess grease. Stir stewed tomatoes, chili beans, kidney beans, pinto beans, black beans, jalapeno pepper, garlic, chili powder, molasses, cumin, bouillon cube, oregano, salt, and cayenne pepper into turkey mixture.

Bring chili to a boil, reduce heat to low, and cover pot. Simmer until vegetables are tender and flavors have blended, about 20 minutes.