Single crystals of Ba8CoRh6O21, grown out of a potassium carbonate flux, were characterized by single-crystal X-ray diffraction and magnetic measurements. X-ray data were collected in a superspace group approach and solved using the JANA2000 software package. Ba8CoRh6O21 represents the first example of a structurally characterized m = 5, n = 3 member of the A(3n+3m)A ' nB3m+nO9m+6n family of 2H hexagonal perovskite related oxides and contains chains consisting of six consecutive RhO6 octahedra followed by one distorted CoO6 trigonal prism. Magnetic measurements were carried out on large aligned single crystals, and a very large magnetic anisotropy in the magnetic susceptibility, persisting up to room temperature, was observed.