Heat a small Dutch oven over medium-high heat. Coat pan with cooking spray. Add venison; cook 3 minutes or until browned, stirring to crumble. Remove from pan with a slotted spoon. Cover and keep warm.
Reduce heat to medium. Add onion, bell pepper, garlic, and jalapeño to pan; cook 10 minutes or until tender, stirring frequently. Stir in chili powder and next 4 ingredients (through black pepper). Add venison, diced tomatoes, chicken broth, and tomato paste, stirring until well combined; bring to a boil. Cover; reduce heat, and simmer 30 minutes. Add red kidney beans; cook, uncovered, 15 minutes.