Scrub potatoes and coarsely grate. Immediately place in a bowl of ice water to keep potatoes from discoloring; let stand for 5 minutes.
Meanwhile, place the onion, carrot, flour, chives, salt, pepper and eggs in a medium bowl and stir well. Drain the potatoes and squeeze out moisture; stir into egg mixture.
Heat 1 tablespoon oil in a large non stick skillet over medium-high heat until very hot. Spoon about 1/4 cup of potato mixture for each pancake into skillet, cooking 4 at a time. Cook for 3 to 4 minutes per side, flattening with the back of a spatula and cooking until golden brown and crisp on both sides. Drain on paper towels. Repeat with remaining oil and potatoes. Serve immediately with chunky applesauce and low-fat sour cream.