  (TaSe$_4$)$_3$I, a compound belonging to the family of quasi-one-dimensional
transition-metal tetrachalcogenides, has drawn significant attention due to a
recent report on possible coexistence of two antagonistic phenomena,
superconductivity and magnetism below 2.5~K (Bera et. al, arXiv:2111.14525).
Here, we report a structural phase transition of the trimerized phase at
temperature, $T~\simeq$~145~K using Raman scattering, specific heat, and
electrical transport measurements. The temperature-dependent single-crystal
X-ray diffraction experiments establish the phase transition from a
high-temperature centrosymmetric to a low-temperature non-centrosymmetric
structure, belonging to the same tetragonal crystal family. The first-principle
calculation finds the aforementioned inversion symmetry-breaking structural
transition to be driven by the hybridization energy gain due to the off-centric
movement of the Ta atoms, which wins over the elastic energy loss.
