Heat a Dutch oven over medium heat. Season the chuck roast with salt and pepper. Add the oil to the pot and sear the chuck roast until browned, 7 to 8 minutes. Remove from the pot, then add the ground beef. Cook until browned, 7 to 8 minutes. Add the garlic and cook for 2 minutes, then return the chuck roast back to the pot with the beer and tomatoes.
Using scissors, snip the guajillo chiles into small strips. Add to the mixture and bring to a boil. Add the chili powder, cumin, oregano and 2 tablespoons salt, then reduce to a simmer and cook for an additional 10 minutes to allow the flavors to combine.
Mix the masa with enough water to form a paste, then add it to the pot. Add the pinto and kidney beans and cook until the chili thickens, 5 to 10 minutes. Adjust the seasoning and simmer for 1 hour.
Serve with fixings such as pico de gallo, sour cream and lime wedges.