Makes about 80 hors d’oeuvres.
Preheat oven to 375° F. and brush 3 large baking sheets generously with some oil.
With a mandoline or other manual slicer cut 1 potato crosswise into 1/8-inch-thick slices. Immediately arrange slices in one layer on 1 baking sheet and brush with some remaining oil. Sprinkle potatoes with dill and salt and pepper to taste.
Bake slices in middle of oven until golden, 15 to 20 minutes, and with a metal spatula immediately transfer to a rack to cool completely. Repeat procedure with remaining potatoes and baking sheets in same manner. Potato chips may be made 3 days ahead and kept in an airtight container at room temperature.
Top potato chips with 1 teaspoon each of caviar and crème fraîche or sour cream, side by side.