ABSTRACT: Halide perovskite (HaP) semiconductors are revolutionizing photovoltaic (PV) solar energy conversion by showing remarkable performance of solar cells made with HaPs, especially tetragonal methylammonium lead triiodide (MAPbI3). In particular, the low voltage loss of these cells implies a remarkably low recombination rate of photogenerated carriers. It was suggested that low recombination can be due to the spatial separation of electrons and holes, a possibility if MAPbI3 is a semiconducting ferroelectric, which, however, requires clear experimental evidence. As a first step, we show that, in operando, MAPbI3 (unlike MAPbBr3) is pyroelectric, which implies it can be ferroelectric. The next step, proving it is (not) ferroelectric, is challenging, because of the material's relatively high electrical conductance (a consequence of an optical band gap suitable for PV conversion) and low stability under high applied bias voltage. This excludes normal measurements of a ferroelectric hysteresis loop, to prove ferroelectricity's hallmark switchable polarization. By adopting an approach suitable for electrically leaky materials as MAPbI3, we show here ferroelectric hysteresis from well-characterized single crystals at low temperature (still within the tetragonal phase, which is stable at room temperature). By chemical etching, we also can image the structural fingerprint for ferroelectricity, polar domains, periodically stacked along the polar axis of the crystal, which, as predicted by theory, scale with the overall crystal size. We also succeeded in detecting clear second harmonic generation, direct evidence for the material's noncentrosymmetry. We note that the material's ferroelectric nature, can, but need not be important in a PV cell at room temperature.