Janice made venison chili today as well.
Here's what I did (pretty much)
In a large, deep frying pan or Dutch oven, heat a generous amount of fat (I would have used suet if I had it, but instead I used a combination of Crisco and corn oil) and brown the chunks of venison you plan to use (no amounts here). Remove to a plate. In the same pan, add a bit more fat (seriously, you need to do this as venison is really lean and will be tough if you don't) and a chopped onion, a few cloves of smashed garlic, and about 10 peppercorns. Cook for a few minutes to soften the onion. Add the meat back to the pan, and add just enough water to cover. Cook, uncovered at a good simmer until tender-about 2 hours. Strain through a sieve into a bowl (you'll want the liquid). Remove venison chunks. Discard onion, garlic, and peppercorns. When cool enough to handle, shred the venison with your fingers. Meanwhile, heat (you guess it) a bit more fat in the same pan (no need to wash it) and cook a couple chopped carrots, more garlic, and beans if you want them (I used tinned pinto, and black beans). Make your spice mix (I used cumin, coriander, ancho chili, paprika, cocoa, black pepper, red pepper flakes, and bay leaves). Dump it into the pan and coat the vegetables and beans well. Add the venison and fry a minute or so. Add chopped tomatoes, their liquid, and bring to a boil. Add the cooking liquid you strained from the venison. Add enough liquid to cover everything by a few inches. Add more water if needed (or tomato juice, if you have it). Bring to a good simmer and cook, stirring occasionally until reduced.
Immediately freeze half the batch to save your husband from eating it all in one sitting.