  The destructive interference of wavefunctions in a kagome lattice can give
rise to topological flat bands (TFBs) with a highly degenerate state of
electrons. Recently, TFBs have been observed in several kagome metals,
including Fe$_3$Sn$_2$, FeSn, CoSn, and YMn$_6$Sn$_6$. Nonetheless, kagome
materials that are both exfoliable and semiconducting are lacking, which
seriously hinders their device applications. Herein, we show that Nb$_3$Cl$_8$,
which hosts a breathing kagome lattice, is gapped out because of the absence of
inversion symmetry, while the TFBs survive because of the protection of the
mirror reflection symmetry. By angle-resolved photoemission spectroscopy
measurements and first-principles calculations, we directly observe the TFB and
a moderate band gap in Nb$_3$Cl$_8$. By mechanical exfoliation, we successfully
obtain monolayers of Nb$_3$Cl$_8$ and confirm that they are stable under
ambient conditions. In addition, our calculations show that monolayers of
Nb$_3$Cl$_8$ have a magnetic ground state, thus providing opportunities to
study the interplay between geometry, topology, and magnetism.
