A new and distinct cultivar of Chrysanthemum plant named ‘Fichrysunaub’, characterized by its upright to outwardly spreading and uniformly and broadly mounded plant habit; moderately vigorous to vigorous growth habit; freely branching habit; dense and full plant form; uniform and freely flowering habit; decorative-type inflorescences with deep red purple-colored ray florets; early to mid-season flowering habit, grown under natural season conditions, plants begin flowering in mid to late August in the United Kingdom; and good garden performance.