Combine first 6 ingredients in a small bowl; set aside.
Boil asparagus in water and 1/2 teaspoon salt 2 minutes or until crisp-tender; drain. Plunge into ice water to stop cooking process; drain.
Combine asparagus, chicken, radishes, onions, and mayonnaise mixture in a large bowl. Sprinkle with cilantro, and toss gently. Cover and chill.
Serve over lettuce leaves, and top each with 6 tomato halves.