Put oven rack in middle position and preheat oven to 400°F. Cut off and discard tops of garlic heads to expose cloves, then brush each head with 1/2 tablespoon oil. Wrap heads together in foil and bake until tender, about 45 minutes. Cool to warm. Squeeze garlic from skins into a food processor and purée with mayonnaise, vinegar, pepper, and salt. Transfer aioli to a bowl and stir in chives. Peel lower two thirds of each asparagus stalk with a vegetable peeler. Cook asparagus in a wide 6- to 8-quart pot of boiling salted water, uncovered, until crisp-tender, about 5 minutes. Drain well in a colander and rinse under cold water until asparagus is cool. Drain and pat dry with paper towels. Serve asparagus with roasted-garlic aioli.