The organic-inorganic hybrid perovskite CH3NH3PbI3 has attracted significant interest for its high performance in converting solar light into electrical power with an efficiency exceeding 20％.Unfortunately,chemical stability is one major challenge in the development of CH3NHaPbI3 solar cells.It was commonly assumed that moisture or oxygen in the environment causes the poor stability of hybrid halide perovskites,however,here we show from the first-principles calculations that the room-temperature tetragonal phase of CH3NH3PbI3 is thermodynamically unstable with respect to the phase separation into CH3NH3I + PbI2,i.e.,the disproportionation is exothermic,independent of the humidity or oxygen in the atmosphere.When the structure is distorted to the low-temperature orthorhombic phase,the energetic cost of separation increases,but remains small.Contributions from vibrational and configurational entropy at room temperature have been considered,but the instability of CH3NH3PbI3 is unchanged.When I is replaced by Br or Cl,Pb by Sn,or the organic cation CH3NH3 by inorganic Cs,the perovskites become more stable and do not phase-separate spontaneously.Our study highlights that the poor chemical stability is intrinsic to CH3NH3PbI3 and suggests that element-substitution may solve the chemical stability problem in hybrid halide perovskite solar cells.