In a large saucepan cook onions and garlic in hot oil for 4 to 5 minutes or until onion is tender. Stir in chicken broth, corn, and pepper. Bring to boiling. Reduce heat and simmer, covered, for 5 minutes.
If desired, stir in chicken; heat through. Pour the eggs into the soup in a steady stream while stirring 2 or 3 times to create shreds. Top each serving with the additional green onion.