Heat a large saucepan over medium heat and coat with cooking spray. Add venison and cook until browned and no longer pink. Remove from pan and keep warm.
Add onion, peppers, and garlic to pan, cooking 10 minutes or until tender, stirring frequently.
Add chili power, salt, cumin, red and black pepper. Add venison back to the pan with tomatoes, chicken broth, and tomato paste, stirring well.
Bring to a boil, cover and reduce heat to low, simmering for 30 minutes.
Remove the lid, and cook an additional 15 minutes. Serve with shredded cheese and sour cream.