Heat oil in a large pot over medium heat. Add onions and cook until soft, about 5 minutes. Stir in garlic and cook for an additional 30 seconds.
Stir in chicken, cumin, oregano, cayenne, salt, and pepper. Cook, stirring often, until chicken browns, about 8 minutes.
Add beans, chili peppers, and stock to pot. Bring to a simmer, cover, and cook for 20 minutes.
Remove pot from heat. Fold yogurt into chili until fully incorporated and serve.