Bring the water, butter and salt to boil over a moderate heat. Add the semolina, and stir until the semolina is well mixed starts to come away from the sides of the saucepan. This will take only about 15 - 30 seconds.
Transfer to a bowl and with a wooden spoon stir in the egg, horseradish and chives and stir firmly until the mixture is smooth. When cool enough, form into small balls.
Bring a pot of salted water to a simmer. Drop the balls of dumplings into the water and cook until they float. About 4 - 5 minutes.