Warm the olive oil in a large pot or Dutch oven set over medium heat.
Stir in the diced onion and cook for about 7–8 minutes, stirring from time to time.
Add the garlic and green chiles, then cook for 2–3 more minutes.
Stir in the cumin, oregano, paprika, salt, and pepper.
Add every remaining ingredient except the chicken. Begin with 2 cups of broth and add more if you want a thinner consistency.
Simmer for a few minutes so the flavors can meld, then remove 1 to 1 1/2 cups and blend until smooth.
Return the blended portion to the pot and stir in the chicken.
Simmer over low heat for 10–15 minutes. For a thinner consistency, stir in an additional 1/2 cup of broth.
Stir in the lime juice. Serve topped with fresh cilantro and tortilla chips, and enjoy!