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Halide perovskite (HP) semiconductors exhibit unique strong coupling betweenthe electronic and structural dynamics. The high-temperature cubic phase of HPsis known to be entropically stabilized, with imaginary frequencies in thecalculated phonon dispersion relation. Similar calculations, based on thestatic average crystal structure, predict a stable tetragonal phase with noimaginary modes. This work shows that in contrast to standard theorypredictions, the room-temperature tetragonal phase of CH$_{3} $NH$_{3}$PbI$_{3}$ is strongly anharmonic. We use Raman polarization-orientation (PO)measurements and \textit{ab initio} molecular dynamics (AIMD) to investigatethe origin and temperature evolution of the strong structural anharmonicitythroughout the tetragonal phase. Raman PO measurements reveal a new spectralfeature that resembles a soft mode. This mode shows an unusual continuousincrease in damping with temperature which is indicative of an anharmonicpotential surface. The analysis of AIMD trajectories identifies two majorsources of anharmonicity: the orientational unlocking of the [CH$_{3}$NH$_{3}$]$^+$ ions and large amplitude octahedral tilting that continuouslyincreases with temperature. Our work suggests that the standard phonon picturecannot describe the structural dynamics of tetragonal CH$_{3} $NH$_{3}$PbI$_{3}$.

The tetragonal phase of CH$_{3}$NH$_{3}$PbI$_{3}$ is strongly anharmonic