  The opening of an energy gap in the electronic structure generally indicates
the presence of interactions. In materials with low carrier density and short
screening length, long-range Coulomb interaction favors the spontaneous
formation of electron-hole pairs, so-called excitons, opening an excitonic gap
at the Fermi level. Excitonic materials host unique phenomenons associated with
pair excitations. However, there is still no generally recognized
single-crystal material with excitonic order, which is, therefore, awaited in
condensed matter physics. Here, we show that excitonic states may exist in the
quasi-one-dimensional material Ta$_2$Pd$_3$Te$_5$, which has an almost ideal
Dirac-like band structure, with Dirac point located exactly at Fermi level. We
find that an energy gap appears at 350 K, and it grows with decreasing
temperature. The spontaneous gap opening is absent in a similar material
Ta$_2$Ni$_3$Te$_5$. Intriguingly, the gap is destroyed by the potassium
deposition on the crystal, likely due to extra-doped carriers. Furthermore, we
observe a pair of in-gap flat bands, which is an analog of the impurity states
in a superconducting gap. All these observations can be properly explained by
an excitonic order, providing Ta$_2$Pd$_3$Te$_5$ as a new and promising
candidate realizing excitonic states.
