Grate potatoes in long strips, using smooth strokes to run potatoes across the grater. Transfer to a large bowl of cold water. Use a slotted spoon to remove potatoes. Drain well and transfer to a second bowl. Reserve soaking liquid. Set reserved liquid aside for 10 minutes to allow the starch to sink to the bottom of the bowl. Carefully pour liquid from the bowl, reserving the milky residue (potato starch).
Using the same method as for potatoes, grate parsnip and carrot. To potatoes add parsnip, carrots, reserved potato starch, chives, egg, salt, and pepper, and mix well.
Preheat oven to 200 degrees. Line a baking sheet with paper towels; set aside. In a heavy nonstick skillet, heat 1/2 inch of oil. Working in batches to accommodate pan size, spoon 1/4 cup of potato mixture into skillet for each pancake. Drop into oil loosely; you should be able to see oil bubbling up in between the individual strands. Fry until golden brown, 2 to 3 minutes per side. Transfer to prepared baking sheet to drain. Sprinkle with salt. Keep warm in oven. Serve hot, with sour cream and lemon slices.