Brown the chicken in a heavy soup pot with a drizzle of olive oil over medium-high heat. Remove from pot.
To the same pot, add a drizzle of olive oil (if pan is dry) over medium-high heat. Add the chopped onion. Sauté about 2 minutes. Add the garlic and ground cumin, and cook an additional 1-2 minutes.
Add broth, chicken, Mexican oregano, red chile powder, and tomatoes. Simmer 5 minutes before adding the green chile, corn, and black beans. Simmer an additional 10 minutes covered. While the soup simmers, prepare the garnishes.
Ladle the chicken tortilla soup into bowls. Garnish with prepared tortilla strips, lime wedges, cheese, and chopped cilantro as desired.
If you use salted chicken broth, you may not want any salt. If you use unsalted chicken broth, start with about ½ teaspoon and season to taste.