Preheat oven to 400 degrees (200 Celsius).
Using a box grater or food processor, coarsely grate potato and remove excess liquid in a kitchen towel. In a bowl, mix potato with smoked salmon and chives.
In a skillet, heat oil and butter over medium heat. Spoon mixture, 2 tablespoons at a time, into pan turning once, until golden, about 2 minutes.
Garnish with half teaspoon crème fraîche or sour cream.
Transfer to a baking sheet, and bake until potato is tender, 8-10 minutes.