Remove fat and ligaments from chuck roast and cut into 1/2-inch cubes.
Heat 1 tablespoon oil in a large pot over medium heat. Add cubed roast. Cook and stir until browned, about 5 minutes. Drain and discard grease. Transfer meat to a bowl and set aside.
Return pot to medium heat. Add remaining oil and vinegar, scraping up any bits at the bottom of the pot. Add onion and bell peppers and cook until onion is translucent, 5 to 10 minutes. Add stock and water. Add diced tomatoes, light kidney beans, dark kidney beans, brown sugar, tomato paste, chili powder, barbecue sauce, ketchup, garlic, cumin, hot sauce, mustard, Worcestershire sauce, and salt. Bring chili to a simmer, about 5 minutes.
