The photovoltaic perovskite, methylammonium lead triiodide [CH3NH3PbI3 (MAPbI(3))], is one of the most efficient materials for solar energy conversion. Various kinds of chemical and physical modifications have been applied to MAPbI(3) towards better understanding of the relation between composition, structure, electronic properties and energy conversion efficiency of this material. Pressure is a particularly useful tool, as it can substantially reduce the interatomic spacing in this relatively soft material and cause significant modifications to the electronic structure. Application of high pressure induces changes in the crystal symmetry up to a threshold level above which it leads to amorphization. Here, a detailed structural study of MAPbI(3) at high hydrostatic pressures using Ne and Ar as pressure transmitting media is reported. Single crystal X-ray diffraction experiments with synchrotron radiation at room temperature in the 0-20 GPa pressure range show that atoms of both gaseous media, Ne and Ar, are gradually incorporated into MAPbI(3), thus leading to marked structural changes of the material. Specifically, Ne stabilizes the high-pressure phase of Ne(x)MAPbI(3) and prevents amorphization up to 20 GPa. After releasing the pressure, the crystal has the composition of Ne(0.97)MAPbI(3), which remains stable under ambient conditions. In contrast, above 2.4 GPa, Ar accelerates an irreversible amorphization. The distinct impacts of Ne and Ar are attributed to differences in their chemical reactivity under pressure inside the restricted space between the PbI6 octahedra.