Combine first 6 ingredients in a large saucepan; bring to a boil. Cook 5 minutes. Add chicken. Cover, reduce heat, and simmer 15 minutes or until chicken is tender. Remove chicken from pan with a slotted spoon. Place chicken on a cutting surface; cover loosely with foil. Let stand 10 minutes; cut chicken into bite-sized pieces.
Return poaching liquid to a boil. Add asparagus; cook 2 minutes or until crisp-tender. Drain and rinse with cold water; drain well. Discard bay leaf and onion. Combine chicken, asparagus, bell pepper, Apple-Kiwi Dressing, and tarragon; toss well to combine.