Combine all the Sauce ingredients in a small bowl and stir well.
Heat a small saucepan over high heat and bring the water to a boil. Add the sliced onion, chicken, and sauce, and cook for 2 minutes, or until the chicken is cooked through. Skim off any scum that forms.
Pour the eggs slowly in a circular motion, covering the chicken. Reduce the heat to a simmer and cover the saucepan with its lid. Cook for 2 minutes, or until the eggs are set. Add the scallions.
To serve, add steamed rice to two bowls and top with the simmered chicken and eggs. Serve immediately.