1. In a heavy 4- to 5-quart flameproof casserole, combine the chicken, ½ cup chopped onions, coriander sprigs, salt and black pepper, and 10 cups of water.
2. Bring to a boil over high heat, meanwhile skimming off the foam and scum that will rise to the surface. Reduce the heat to low, and cover the casserole.
3. Simmer the chicken for 30 minutes, or until it is tender but not falling apart. Transfer the chicken to a platter and cover it with foil to keep it warm. Drop the plantains and yuca into the stock remaining in the casserole, cover and cook over moderate heat for 20 minutes.
4. Add the squash and turmeric, cover, and cook for 20 minutes longer. Remove the coriander sprigs. Return the chicken to the casserole and simmer for 4 to 5 minutes, or just enough to heat it through. Taste for seasoning.
5. To make the sauce, pour the vinegar, water, olive oil, salt and sugar into a small sauce bowl. Beat vigorously with a whisk or fork until the ingredients are thoroughly combined. Stir in the chili and fresh chopped coriander and taste for seasoning.
6. Serve the soup in large bowls, each topped with a few slices of avocado. Pass the sauce separately to be added to the soup at each diner's discretion.
