Combine the first 8 ingredients (water through hominy) in the crock of a 6-quart slow cooker.
Add chicken breasts to stock mixture; submerge in liquid.
Cover and cook on LOW for 6 - 8 hours.
Carefully remove chicken from cooker and let cool for a few minutes. When chicken is cool enough to handle, remove bones, and shred or roughly chop chicken into large pieces.
Return chicken to slow cooker; stir in tomatillos, cilantro, juice, and salt to taste.
Divide soup among 6 bowls; top evenly with radishes, avocado and tortilla strips.
Recipe inspired by Cooking Light Chicken Posole