Heat oil in a 3-quart saucepan over medium heat.
Add onions and cook until soft, 6–7 minutes.
Add garlic and cook, stirring, an additional 2 minutes.
Add chicken, cumin, and oregano and cook, stirring, until just cooked through, 5 minutes.
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.
Divide among 4 bowls and serve immediately with tortilla chips alongside, if desired.
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