Heat the oil in a large, heavy pot over medium heat. Sauté the onions in it for about 10 minutes, until they have turned a golden yellow color. Add the celery and garlic and cook until lightly colored, about 4 minutes. Add the ground beef and stir until it breaks into chunks.
Thoroughly fold in the tomatoes with their juice, the stock and the tomato paste. Stir in all the seasoning ingredients and herbs.
Cook the whole thing without the lid for 1 1/4 hours, simmering gently. Add the beans to the pot and simmer everything quietly for another 20-30 minutes so the flavors blend. Serve the venison chili boiling hot.