Combine onion, celery, ginger, garlic, and peppercorns in a large heavy pot. Add chicken, placing breasts on top. Add 6 quarts water (preferably filtered or spring water); bring to a boil over medium-high heat. Cover with lid slightly ajar. Reduce heat to low; simmer until chicken breasts are just cooked through, about 30 minutes. Transfer chicken breasts to a plate; let cool, then cover and chill. Continue to simmer soup, uncovered, until broth is fully flavored, about 2 ½ hours longer. Return breasts to soup to rewarm, about 5 minutes.