In large, heavy pot over medium heat, heat oil. Reserve 1/4 cup onion for garnish; add remaining onion to pot and season with salt. Saute until translucent, about 5 minutes.
Increase heat to medium-high; add pork chorizo and break it apart with spoon. Cook chorizo undisturbed until deeply browned and cooked through, 3-5 minutes. Add smoked paprika and oregano; cook 30 seconds, or until fragrant.
Pour in salsa and scrape up browned bits from bottom of pan. Bring to simmer 1-2 minutes, allowing it to thicken slightly then add stock and bring to simmer.
Stir in diced chicken and hominy. Decrease heat to medium and cook 8-10 minutes until chicken is cooked through. Taste and season with more salt, if necessary. Remove from heat.
Serve bowls of pozole with reserved onion, lime wedges, crumbled queso fresco and chopped cilantro.