Place all ingredients except hominy and garnishes into a 5-quart or larger slow cooker. Cook on low for 6 to 8 hours, until the chicken is tender and cooked through.
Take chicken out of slow cooker and let cool for a few minutes. Pull meat off the bone and shred with two forks. Discard skin and bones and return to the slow cooker along with hominy and cook another 30 minutes. Season with salt and pepper.
Ladle pozole into bowls and garnish with any combination of sliced radishes, shredded cabbage, fresh cilantro, tortilla strips, and lime.
Per serving: 567 calories, 16 grams fat (4 grams saturated fat), 42 grams total carbohydrates, 8 grams fiber, 59 grams protein.
Note: For extra spice, leave in the poblano pepper seeds.