- Bring water to boil in 2-quart saucepan. Add chiles and steep until tender. Stem and seed chiles.
- Meanwhile, heat olive oil in large pot and sauté onion, tomatoes, garlic, and oregano. Continue to cook, stirring, until onion is translucent.
- Add water and chiles and bring to simmer. Turn off heat, cool slightly, and then transfer mixture to blender. Purée until smooth. Transfer purée back to pot, add chicken, and cook for another 10 minutes over medium-low heat.
- In separate skillet, cook chorizo until crispy. Drain fat and set aside.
- Heat ½-inch canola oil in deep skillet. When oil is hot, fry tortilla strips until golden. Use slotted spatula to transfer to paper towel-lined plate.
- Season soup to taste. To serve, ladle into 4 bowls and garnish with crispy tortilla strips, shredded cheese, avocado, chorizo, and generous squeeze of lime.