Bring water to a boil in a large saucepan. Add salt and rice wine vinegar. Reduce the heat, carefully crack the eggs and slide them one by one into the simmering water. Poach the eggs for 1 minute, then remove and keep warm.
In another saucepan, bring the chicken broth to the boil. Add the leek, broccoli, mushrooms, chicken and rice wine. Season with the chilli sauce and cook for 10-15 minutes. Add the poached eggs to the soup. Cook for 2 minutes.
Put eggs and soup on plates. Dust with chili powder and serve immediately.