Combine first 4 ingredients; toss well. Combine balsamic vinegar and next 5 ingredients; stir well. Pour vinegar mixture over chicken mixture; toss lightly. Cover and chill.
Cut each cantaloupe in half; remove and discard seeds. If necessary, cut a thin slice from bottom of each melon half so that it will sit flat. Spoon chicken mixture evenly into melon halves. Garnish with lime wedges, if desired.