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Methylammonium lead iodide perovskite can make high-efficiency solar cells, which also show an unexplained photocurrent hysteresis dependent on the device-poling history. Here we report quasielastic neutron scattering measurements showing that dipolar CH₃NH₃⁺ ions reorientate between the faces, corners or edges of the pseudo-cubic lattice cages in CH₃NH₃PbI₃ crystals with a room temperature residence time of ∼14 ps. Free rotation, π-flips and ionic diffusion are ruled out within a 1–200-ps time window. Monte Carlo simulations of interacting CH₃NH₃⁺ dipoles realigning within a 3D lattice suggest that the scattering measurements may be explained by the stabilization of CH₃NH₃⁺ in either antiferroelectric or ferroelectric domains. Collective realignment of CH₃NH₃⁺ to screen a device’s built-in potential could reduce photovoltaic performance. However, we estimate the timescale for a domain wall to …