Heat the oil in a large stockpot over medium-low heat. Add the scallions and cook for 5 minutes, stirring frequently.
Add the ginger, zucchini, and chicken stock. Raise the heat to high and bring the soup to a low boil. Reduce the heat to medium-low and simmer, covered, for 10 minutes, or until the zucchini is tender.
Remove the pot from the heat. Use an immersion blender to puree the soup in the pot, or transfer the soup to a blender, being careful not to burn yourself, and puree it in batches until smooth. Let the soup chill in the refrigerator for at least 2 hours, or until cold, before serving