In a large dutch oven or stock pot, heat oil over medium-high until shimmering. Add in the onions, bell pepper, chili powder, cumin, oregano, thyme, paprika and salt, and pepper. Cook until vegetables have softened, about 7-10 minutes.
Add in the garlic and cook until fragrant, about 30 seconds. Add in the venison and cook until it is no longer pink, about 5-6 minutes. Season with salt and pepper.
Add in the kidney beans, tomatoes, green chilies, and tomato paste. Bring the mixture to a boil then reduce to low and cover, simmering for 45 minutes.
Remove the lid and continue to simmer for an additional 10 minutes. Season with salt and pepper. Place in bowls and top with shredded cheese, sliced green onions, sour cream, and sliced radishes.