Remove stem from chile; cut chile in half lengthwise, and discard seeds. Combine chile and vinegar in a blender, and process until smooth; set aside.
Bring broth to a simmer in a large saucepan; add radish, and cook 5 minutes. Add chile mixture, chicken, and next 3 ingredients; simmer 5 minutes or until chicken is done. Stir in rice; garnish with cilantro, if desired.