In a 6-quart stockpot, melt the butter over medium-high heat. Add the ground venison and chop it up, stirring occasionally, until the meat has begun to brown. Add the garlic and onion and cook for 7 minutes. or until the venison has browned.
Add the green, red, and jalapeno peppers. Stir to combine and cook for 3 minutes, until the peppers have begun to soften.
Add the seasonings to the cooked meat and stir to combine. Saute for 2 minutes to allow the flavors to blend into the venison.
Stir in the canned tomatoes with their juice, tomato sauce, and tomato paste. Bring to a boil, then reduce the heat to low. Simmer for 30 minutes, until the chili has reduced and thickened some.