Methylammonium lead triiodide (MAPI) has emerged as a high-performance photovoltaic material. Common understanding is that at room temperature it adopts a tetragonal phase and it only converts to the perfect cubic phase around 50-60 ºC. Most MAPI films are prepared using a solution-based coating process, yet they can also be obtained by vapor phase deposition methods. Vapor phase processed MAPI films have significantly different characteristics compared to their solvent processed analogous, such as a relatively small crystal grain sizes and short excited state lifetimes. Yet solar cells based on vapor phase processed MAPI films exhibit high power conversion efficiencies. Surprisingly, after detailed characterization we find that our vapor phase processed MAPI films adopt a cubic crystal structure at room temperature that is stable for weeks, even in ambient atmosphere. Furthermore, we demonstrate that by tuning the deposition rates of both precursors during co-deposition it is possible to vary the perovskite phase from cubic to tetragonal at room temperature. Our finding challenges the common belief that MAPI is only stable in tetragonal phase at room temperature. Additionally, these findings can be used to explain the somewhat unexpected high performance of solar cells based on vacuum processed MAPI films with sub 100 nm grain sizes and excited state lifetimes < 100 nanoseconds.