Combine first 8 ingredients in a 5-quart electric slow cooker.
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.
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.
Ladle chili into bowls. Top with cheese, green onions, and olives, if desired.