1. Heat oil in a 3-quart saucepan over medium heat.
2. Add onions and cook until soft, 6–7 minutes.
3. Add garlic and cook, stirring, an additional 2 minutes.
4. Add chicken, cumin, and oregano and cook, stirring, until just cooked through, 5 minutes.
5. Add broth, tomatoes, hominy, green chile, salt, and pepper and bring to a boil. Reduce heat, skimming foam from top of soup, and simmer 10 minutes, until liquid has thickened slightly.
6. Divide among 4 bowls and serve immediately with tortilla chips alongside, if desired.