This stock, and the one for the fish soup that follows, can be made several weeks in advance and frozen. To use, thaw, and bring just to a boil; proceed to step three.
Remove excess fat from chicken parts, and rinse; transfer to a large stockpot. Add all remaining ingredients, except salt, tortellini, and chives. Add 4 quarts water, and bring to a boil. Skim scum from stock as it rises.
Reduce heat to medium. Simmer 2 hours; skim scum as it rises. Pass through fine strainer; discard solids. Skim fat; season with salt.
Bring large pot of salted water to a boil. Add tortellini; cook until al dente, about 8 minutes. Pour soup into 12 very small serving vessels, such as sake cups. Place a tortellini in each; garnish with 2 chive sprigs. Serve immediately, and refill as needed.