Arrange beets in a single layer on a lightly greased baking sheet; bake at 425° for 40 to 45 minutes or until tender, stirring every 15 minutes. Cool beets completely.
Whisk together oil, vinegar, 1/4 teaspoon salt, and 1/4 teaspoon ground pepper in a small bowl.
Peel beets, and cut into wedges. Toss together beets, 1/2 cup vinaigrette, remaining 1/4 teaspoon salt, and remaining 1/4 teaspoon ground pepper; set aside.
Snap off tough ends of asparagus, discarding ends; cook asparagus in boiling water to cover 1 to 2 minutes or until crisp-tender. Plunge into ice water to stop the cooking process, and drain. Combine asparagus and 1/2 cup vinaigrette; set aside.
Cut cheese into 6 equal slices. Place 1 cheese slice in a 3-inch round cutter or ring mold; sprinkle with 1/2 teaspoon chives. Press chives into cheese; remove cutter. Repeat procedure with remaining cheese and 2 1/2 teaspoons chives.
Arrange asparagus over cheese. Surround with beets, and drizzle with remaining vinaigrette. Sprinkle with cracked pepper and chives, if desired; serve with salad greens, if desired.