Combine first 6 ingredients in a large stock pot. Bring to a boil. Reduce heat; cover and simmer 1 1/2 hours. Remove chicken and soup bone from broth; cool slightly. Remove meat from bones; chop meat into bite-size pieces. Discard bones and red pepper pod.
Return meat to broth. Stir in remaining ingredients. Bring to a boil. Reduce heat; cover and simmer 30 minutes. Uncover and simmer an additional 30 minutes.
Ladle stew into individual soup bowls. Serve hot with cornbread, if desired.