  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.
