A well-established way to find novel Majorana particles in a solid-state system is to have superconductivity arising from the topological electronic structure. To this end, the heterostructure systems that consist of normal superconductor and topological material have been actively explored in the past decade. However, a search for the single material system that simultaneously exhibits intrinsic superconductivity and topological phase has been largely limited, although such a system is far more favorable especially for the quantum device applications. Here, we report the electronic structure study of a quasi-one-dimensional (q1D) superconductor TaSe$_3$. Our results of angle-resolved photoemission spectroscopy (ARPES) and first-principles calculation clearly show that TaSe$_3$ is a topological superconductor. The characteristic bulk inversion gap, in-gap state and its shape of non-Dirac dispersion concurrently point to the topologically nontrivial nature of this material. The further investigations of the Z$_2$ indices and the topologically distinctive surface band crossings disclose that it belongs to the weak topological insulator (WTI) class. Hereby, TaSe$_3$ becomes the first verified example of an intrinsic 1D topological superconductor. It hopefully provides a promising platform for future applications utilizing Majorana bound states localized at the end of 1D intrinsic topological superconductors.
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