Heat olive oil in a large pot or Dutch oven over medium heat. Add diced onion and cook for 4-5 minutes until softened. Add minced garlic and cook for another minute until fragrant.
Add chicken breasts, beans, green chiles, chicken broth, cumin, oregano, and cayenne pepper (if using) to the pot. Bring to a boil, then reduce heat and simmer for 20-25 minutes until chicken is cooked through.
Remove chicken from the pot and shred it using two forks. Return shredded chicken to the pot.
Remove pot from heat and stir in sour cream and shredded cheese until melted and creamy. Season with salt and pepper to taste.
Ladle into bowls and serve with your favorite toppings like crushed tortilla chips, fresh cilantro, extra cheese, or a squeeze of lime. Serve with warm cornbread for a complete meal!