1. Combine first 8 ingredients in a 5-quart electric slow cooker.
2. Place turkey on top of vegetables in slow cooker. Add hominy and tomatoes to slow cooker. Cover and cook on LOW for 5 1/2 hours.
3. Remove turkey from slow cooker; cool 10 minutes. Skim solidified fat from surface; discard. Separate turkey into large chunks with 2 forks. Return turkey to slow cooker. Cover and cook on HIGH for 10 minutes or until thoroughly heated.
4. Ladle chili into bowls. Top with cheese, green onions, and olives, if desired.