CH 3 NH 3 PbI 3 is a hybrid organic-inorganic material with a perovskite structure and a temperature-dependent polymorphism whose origins are still unclear. Here we perform ab initio molecular dynamics simulations in order to investigate the structural properties and atom dynamics of CH 3 NH 3 PbI 3 at room temperature. Starting from different initial configurations, we find that a single-crystalline system undergoes a spontaneous ordering process which brings the ions to alternately point towards the center of two out of the six faces of the cubic framework, ie towards the< 100> and< 010> directions. This bidirectional ordering gives rise to a preferential distortion of the inorganic lattice on the a-b plane, shaping the observed tetragonal symmetry of the system. The process requires tens of picoseconds for CH 3 NH 3 PbI 3 supercells with just eight ions.