I use diced tomatoes in my chili, I would never use stewed tomatoes, the flavor isn't fresh enough. Other uses for ground venison are meatloaf and meatballs. I do not get ground meat, I have cubes made instead and I use the cubes for chili and stew.
Try crushed tomatoes and tomato paste like tfabarcher35 said, or just use your favorite spaghetti sauce. It will be a bit thicker than usual Chili and you'll need more Chili powder to counter the sweetness of most spaghetti sauces, but that's the way I alway make mine, and I love it.
I don't know about the other guys, but what I like to do follows these procedures, more or less:
In a stock pot:
Brown 1lb of ground beef or venison, remove
Saute 1 medium sized onion chopped, remove
Saute 2 green bell peppers chopped, remove
**I remove them all because they finish at different times and I don't want one part mushy while the other is hard**
Now everybody back in the pool!!
Along with a jar of spaghetti sauce (your favorite is fine)
All the sauteed ingredients
Add one can of mushrooms
Salt, pepper, and Chili Powder to taste
Simmer for 30 minutes or so
**The spice will vary depending on how spicy you like it and how sweet the spaghetti sauce is**
That's it. For my recipe there really isn't a wrong way to do it. I've put everything from mushrooms, to peppers, to carrots, you name it. It's kind of a spicy/meaty/tomato based/vegetable soup sometimes, but it's good!!