The True Texas Chili recipe from Epicurious.com is a good Texas chili recipe for entering in a cook-off. True Texas style chili has no beans or tomatoes -- only homemade chili paste, beef and a few additional flavorings.
Place 6 to 8 dried, whole guajillo or pasilla chile peppers in a large straight-sided skillet over medium-low heat, and slowly roast them two to three minutes until they are fragrant. Be careful not to burn them, which makes the peppers bitter. Remove the peppers to a bowl, cover them with very hot water, and soak the them until soft. Drain the chiles, cut out the stems, split them, and remove the seeds.
Mix the chiles with 1 1/2 teaspoons of ground cumin seed, one-half teaspoon of ground black pepper, 1 tablespoon of salt and 1/4 cup of water in a blender, and puree until a smooth, slightly fluid paste forms, adding water as necessary. Set the paste aside.
Trim and cube 2 1/2 pounds of boneless beef chuck, and cut it into 3/4-inch cubes. Brown the beef and a small amount of vegetable oil in the skillet on medium-high, and remove it to a separate bowl.
Reduce the skillet to medium-low, and let it cool slightly before adding 1 tablespoon of vegetable oil, 1/3 cup of finely chopped onions and 3 minced garlic cloves. Cook the mixture gently for three to four minutes, and then stir in 2 cups of beef stock and 2 cups of water. Slowly whisk in 2 tablespoons of masa harina. Stir in the chile paste and the beef, and simmer until the meat is tender, about two hours.
Stir in 1 tablespoon of firmly packed brown sugar and 1 1/2 tablespoons of white vinegar, and simmer 10 more minutes. Let stand and thicken before serving.