Combine venison with spices. Heat stock-pot or soup pan, add oil to hot pan and cook venison until meat is not pink (try not to overcook meat, it will cook more later).
Remove venison from heat and place into separate bowl. Using the same pan, heat oil and sauté onions and peppers for 3- five minutes. Add garlic and allow to cook 1 minute. Add chicken broth, hominy, tomatoes and venison back to the pan.
Bring to a boil, reduce to a simmer and allow to heat for 10-15 minutes.