The high power conversion efficiency of the hybrid CH3NH3PbX3 (where X = I, Br, Cl) solar cells is believed to be tightly related to the dynamics and arrangement of the methylammonium cations. In this Letter, we propose a statistical phase transition model which accurately describes the ordering of the CH3NH3+ cations and the whole phase transition sequence of the CH3NH3PbI3 perovskite. The model is based on the available structural information and involves the short-range strain-mediated and long-range dipolar interactions between the cations. It is solved using Monte Carlo simulations on a three-dimensional lattice allowing us to study the heat capacity and electric polarization of the CH3NH3+ cations. The temperature dependence of the polarization indicates the antiferroelectric nature of these perovskites. We support this result by performing pyrocurrent measurements of CH3NH3PbX3 (X = I, Br, Cl) single crystals. We also address the possible occurrence of the multidomain phase and the ordering entropy of our model.