Peel oranges, and cut each crosswise into 5 slices.
Place spinach on a large platter. Spoon beets onto spinach, and arrange orange slices on beets. Heat oil in a nonstick skillet over medium-high heat. Add shallots, and sauté 1 minute or until tender. Stir in vinegar and pepper; drizzle over salad. Sprinkle salad with chives and walnuts.