Rinse the rice well with cold water and let drain 30 minutes.
Combine the rice and water in a saucepan. Cover tightly and boil 15 minutes, then reduce heat to low and let simmer 5 more minutes until water is absorbed.
Cut the chicken breast into bite sized pieces. In a saucepan, place the chicken, sake, 1/2 teaspoon sugar, salt to taste, 1 teaspoon mirin and 1/2 teaspoon soy sauce. Cook until chicken is just done, about 5 minutes.
In another saucepan combine dashi, remaining soy sauce, sugar and mirin. Simmer 5 minutes. Add the chicken, onion and watercress and simmer a few minutes.
Beat the egg and add to the chicken. Cook fifteen seconds, stirring, until egg is just set. Put the rice in a bowl and top with the chicken.