Add the chicken thighs to the bottom of your 6-quart slow cooker.
Pour in the chicken stock, and layer on the hominy, green chiles, onion, poblano pepper, garlic, cumin, and oregano. Sprinkle with salt and pepper.
Cover with the lid, set the slow cooker to low, and cook for 6–8 hours.
Once the chicken is fully cooked, remove it from the slow cooker and let it cool slightly. Discard the bones and shred the meat into bite-sized pieces.
Stir the shredded chicken back into the slow cooker along with the tomatillos, chopped cilantro, and lime juice. Adjust seasonings to taste.
Ladle the posole into bowls and garnish with your favorite toppings like cabbage, radish, queso fresco, tortilla chips, and lime wedges.