Chill chicken broth; skim off any fat. Section oranges, working over a bowl to catch juices. Cut sections into bite-size pieces.
In a large mixing bowl combine orange pieces and reserved orange juice, tomatoes, tomato juice, cucumber, green pepper, shallot, basil, wine vinegar, garlic, ground red pepper, and black pepper. Add broth; stir until thoroughly combined. Cover and chill for 2 to 24 hours.
To serve, ladle into chilled soup bowls or mugs. If desired, garnish with additional basil. Makes 4 to 6 servings.