High-quality single crystals of perovskite-like (CH3NH3)(3)Bi2I9 hybrids have been synthesized, using a layered-solution crystal-growth technique. The large dielectric constant is strongly affected by the polar ordering of its constituents. Progressive dipolar ordering of the methylammonium cation upon cooling below 300 K gradually converts the hexagonal structure (space group P6(3)/mmc) into a monoclinic phase (C2/c) at 160 K. A well-pronounced, ferrielectric phase transition at 143 K is governed by in-plane ordering of the bismuth lone pair that breaks inversion symmetry and results in a polar phase (space group P2(1)). The dielectric constant is markedly higher in the C2/c phase above this transition. Here, the bismuth lone pair is disordered in plane, allowing the polarizability to be substantially enhanced. Density functional theory calculations estimate a large ferroelectric polarization of 7.94 mu C/cm(2) along the polar axis in the P2(1) phase. The calculated polarization has almost equal contributions of the methylammonium and Bi3+ lone pair, which are fairly decoupled.