Brown ground beef and stew meat in a large skillet; drain any drippings. Transfer beef to a large pot and stir in all ingredients except the masa. Bring to a boil and simmer, uncovered, for 1½ to 2 hours, stirring occasionally.
Combine masa and ¼ cup water and stir into chili. Simmer for an additional 30 minutes. Serve with your favorite chili toppings.