For the radish salad, peel the white radish and brush the red radish well under cold running water. Wash the cucumber too. Finely grate the radish and cucumber on a raw vegetable grater and mix together in a large bowl.
For the radish sauce, stir the sour cream with salt, pepper, vinegar and oil in a bowl until smooth, pour onto the radish salad and mix everything well. Season to taste with salt and pepper.
Arrange the radish salad with the cucumber on plates side by side, sprinkle with the chives and serve.