1.Place chicken in medium saucepan of boiling water; return to a boil. Reduce heat; simmer, covered, about 10 minutes or until chicken is cooked through. Cool chicken in liquid 10 minutes. Remove chicken; discard liquid (or keep for another use). Shred chicken coarsely.
2.Cook noodles in large saucepan of boiling water, uncovered, until just tender; drain. Rinse under cold water; drain. Cover; refrigerate until cool.
3.Meanwhile, place ingredients for mirin dressing in screw-top jar; shake well.
4.Place chicken and noodles in large serving bowl with radish, cucumber, onion and dressing; toss gently to combine. Top with seaweed; serve immediately.
All ingredients can be prepared ahead of time and stored separately, covered, in the refrigerator. Use scissors to cut the seaweed into fine shreds.Note