The synthesis and investigation of the physicochemical properties of a novel one-dimensional (1D) hybrid organic-inorganic perovskitoid templated by the 1,1,1-trimethylhydrazinium (Me3Hy+) cation are reported. (Me3Hy)[PbI3] crystallizes in the hexagonal P63/m symmetry and undergoes two phase transitions (PTs) during heating (cooling) at 322 (320) and 207 (202) K. X-ray diffraction data and temperature-dependent vibrational studies show that the second-order PT to the high-temperature hexagonal P63/mmc phase is associated with a weak change in entropy and is related to weak structural changes and different confinement of cations in the available space. The second PT to the low-temperature orthorhombic Pbca phase that corresponds to the high change in entropy and dielectric switching is associated with an ordering of the trimethylhydrazinium cations, re-arrangement and strengthening of hydrogen bonds, and slightly shifted lead-iodide octahedral chains. The high-pressure Raman data revealed two additional PTs, one between 2.8 and 3.2 GPa, related to the symmetry decrease, ordering of the cations, and inorganic chain distortion, and the other in the 6.4-6.8 GPa range related to the partial and reversible amorphization. Optical studies revealed that (Me3Hy)[PbI3] has a wide band gap (3.20 eV) and emits reddish-orange excitonic emission at low temperatures with an activation energy of 65 meV.