1/4 cup plus 1 tablespoon extra-virgin olive oil
1 large yellow onion, halved lengthwise and thinly sliced crosswise
2 teaspoons dried oregano
3/4 teaspoon chile powder
1/2 teaspoon ground cumin
3 pounds chicken drumsticks and thighs
4 cups chicken stock
Salt and freshly ground pepper
Two 15-ounce cans hominy, drained and rinsed
1 pound plum tomatoes, chopped
1 small red onion, finely chopped
1 tablespoon fresh lime juice
Lime wedges, diced radishes, sliced scallions, shredded romaine, cilantro leaves and tortilla chips, for serving
In a large pot, heat 1/4 cup of the oil. Add the yellow onion and cook over moderately high heat, stirring, until beginning to soften, 3 minutes. Stir in the oregano, chile powder and cumin. Add the chicken and stir to coat with the seasonings. Add the chicken stock and 2 cups of water, season with salt and pepper and bring to a boil. Simmer over low heat until the chicken is cooked through, 30 minutes.
Using tongs, transfer the chicken to a plate. Let cool, then coarsely shred the meat; discard the skin and bones. Add the shredded chicken and hominy to the broth and simmer over low heat for 15 minutes; skim any fat.
In a bowl, toss the tomatoes, red onion, lime juice and the remaining 1 tablespoon of oil. Season the salsa with salt and hot sauce.
Serve the posole with the salsa, limes, radishes, scallions, romaine, cilantro and chips.
MAKE AHEAD The posole can be refrigerated for up to 3 days.