Step 1Brown the chicken in a stock pot with the oil over medium-high heat, about 5 minutes.
Step 2Add the shallots, celery, carrot, sugar, curry powder, turmeric, tarragon, cayenne pepper and bananas. Cook until the vegetables are tender and the bananas are soft, about 10 minutes. Add the tomato sauce and chicken stock. Bring to a boil and simmer until the chicken is cooked and the flavors have melded, 30 minutes.
Step 3Combine the cornstarch with a little water and add it to the soup. Simmer the soup to thicken slightly, another 2 to 3 minutes, and add salt to taste. Serve hot.