Heat 2 teaspoons olive oil in a 4-quart pot over medium-high heat. Saute chicken until no longer pink in the center, 5 to 6 minutes. Remove from the pot.
Heat remaining 1 teaspoon oil in the same pot over medium-high heat. Saute onion and garlic for 3 minutes. Add chiles, cumin, and oregano; cook for 3 minutes more. Add chicken, white beans, and chicken broth. Bring to a boil. Reduce heat and simmer for 10 minutes. Add Monterey Jack cheese and sour cream; cook and stir until cheese melts, 3 to 5 minutes.