Season the chicken with 1 teaspoon of the oregano, 1 teaspoon salt and some black pepper; set aside.
Heat the oil in a large Dutch oven or pot over medium heat. Add the onions, jalapenos and garlic, and cook, stirring frequently, until soft, about 6 minutes.
Transfer the mixture to a blender. Add 2 cups of the broth, the chiles, cilantro and the remaining 1 teaspoon oregano, and puree until smooth.
Return the mixture to the Dutch oven. Add the hominy and the remaining 6 cups broth, and bring to a simmer. Continue to cook, stirring occasionally, until the sauce thickens and turns deep green, about 12 minutes. Add the seasoned chicken, and simmer until tender and cooked through, about 12 minutes more.
Let the soup cool to room temperature, then divide among four 1-quart containers and freeze for up to 1 month.
To reheat: Let the soup thaw in the refrigerator overnight. Bring to a simmer over medium-low heat, stirring frequently, until heated through. Thin with a little water if desired, and adjust the seasoning with salt.
Garnish with avocado, radishes and/or corn chips if using.
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