  Chow stability is one notion of Mumford's Geometric Invariant Theory for
studying the moduli space of polarized varieties. Kapranov, Sturmfels and
Zelevinsky detected that Chow stability of polarized toric varieties is
determined by its inherent {\it secondary polytope}, which is a polytope whose
vertices correspond to regular triangulations of the associated polytope
\cite{KSZ}. In this paper, we give a purely convex-geometrical proof that the
Chow form of a projective toric variety is $H$-semistable if and only if it is
$H$-polystable with respect to the standard complex torus action $H$. This
\emph{essentially} means that Chow semistability is equivalent to Chow
polystability for any (not-necessaliry-smooth) projective toric varieties.
