A new and distinct cultivar of Chrysanthemum plant named ‘Fichryrainsun’, characterized by its upright to outwardly spreading and uniformly mounded plant habit; moderately vigorous growth habit; freely branching habit; dense and full plant form; uniform and freely flowering habit; large semi-decorative type inflorescences with red and yellow bi-colored ray florets; response time about 51 days under controlled photoperiodic treatments; and good postproduction longevity.