A model for the spontaneous generation of the chiral generations of quarks and leptons is presented in a framework of supersymmetric theory based on the noncompact horizontal gauge symmetry G(H) = SU(1, 1) which governs, together with the standard gauge symmetry SU(3) x SU(2) x U(1), the world in a vectorlike manner. Quarks, leptons and Higgses are assigned to infinite dimensional unitary representations of SU(1, 1). The model reproduces quite naturally the hierarchical structure of their Yukawa coupling matrices.