Hold each asparagus spear by the tip end. Shave asparagus into ribbons with a vegetable peeler to measure 3 cups. Reserve asparagus tips for another use. Combine asparagus and tomatoes in a medium bowl.
Combine chives and next 6 ingredients (through 1/4 teaspoon salt), stirring with a whisk. Drizzle over the asparagus mixture, tossing gently to coat. Top with goat cheese.