A high-index topological insulator thin film, Bi2Se3(221), is grown on a faceted InP(001) substrate by molecular-beam epitaxy (see model in figure (a)). Angle-resolved photoemission spectroscopy measurement reveals the Dirac cone structure of the surface states on such a surface (figure (b)). The Fermi surface is elliptical (figure (c)), suggesting an anisotropy along different crystallographic directions. Transport studies also reveal a strong anisotropy in Hall conductance.