1. Combine the chicken and fresh stock (or canned beef stock and water) in a heavy 6- to 8-quart casserole and bring to a boil over high heat.
2. With a large spoon, skim off the foam and scum as they rise to the surface. Reduce the heat to low, cover partially, and simmer for 45 minutes.
3. Skim as much fat from the soup as possible, then add the tomatoes, corn, yams, boiling potatoes, pumpkin (or squash), peas, chilies, salt and pepper.
4. Bring the "saucochi" to a boil again, reduce the heat and simmer partially covered for about 20 minutes longer; or until the chicken and vegetables are tender but still intact.
5. Taste the soup for seasoning and stir in the chives. Serve at once from a heated tureen or individual soup plates.
