Rinse the fish and pat dry. With your sharpest knife, remove the brown flesh on the skinned side, not too much, just a little. Cut the fish into 1/4-inch (6-mm) cubes, transferring the pieces to a cool bowl as you go.
Add about 1 teaspoon lemon juice, the chives, shallot, and a generous pinch each of salt and pepper and stir. Taste and rectify if need be, then mix in the oil.
Serve within 15 minutes. Shave horseradish to order.
