1. In a medium-sized stockpot, heat two tablespoons oil over medium heat.
2. Add onion, celery, carrot, garlic and salt. Cook until soft, stirring occasionally, about eight minutes. Add the chicken broth and water. Bring to a boil, then reduce the heat to medium low and simmer for five minutes.
3. Chop the chestnuts. Add to the pan and simmer until the chestnuts and vegetables are tender, about 10 more minutes.
4. Puree soup in a blender until smooth. Add soy or almond milk and salt to taste. Keep warm.