  Let \Delta\subset \mathbb{R}^n be an n-dimensional Delzant polytope. It is
well-known that there exist the n-dimensional compact toric manifold X_\Delta
and the very ample (\mathbb{C}^\times)^n-equivariant line bundle L_\Delta on
X_\Delta associated with \Delta. In the present paper, we show that if
(X_\Delta,L_\Delta^i) is Chow semistable then the sum of integer points in
i\Delta is the constant multiple of the barycenter of \Delta. Using this result
we get a necessary condition for the polarized toric manifold
(X_\Delta,L_\Delta) being asymptotically Chow semistable. Moreover we can
generalize the result of Futaki, Sano and the author to the case when X_\Delta
is not necessarily Fano.
