  We demonstrate, using first-principles calculations, that the electronic
structure of FeSe$_{1-x}$Te$_{x}$ ($x$=0.5) is topologically non-trivial,
characterized by an odd $\mathbb Z_2$ invariant and Dirac cone type surface
states, in sharp contrast to the end member FeSe ($x$=0). This topological
state is induced by the enhanced three-dimensionality and spin-orbit coupling
due to Te substitution (compared to FeSe), characterized by a band inversion at
the $Z$ point of the Brillouin zone, which is confirmed by our ARPES
measurements. The results suggest that the surface of FeSe$_{0.5}$Te$_{0.5}$
may support a non-trivial superconducting channel in proximity to the bulk.
