Stir together chicken, half the green chilies and next four ingredients in slow cooker. Cover and cook four hours.
After four hours, stir together remaining green chilis, muffin mix and eggs; set aside.
Remove lid, shred chicken inside cooker with two forks.
Spoon cornbread mix evenly over mixture and return lid to cooker.
Cook additional 1 1/2 hours.
Sprinkle cheese over cornbread if desired and let melt five minutes.