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Donaldson proved that if a polarized manifold $(V,L)$ has constant scalar curvature Kähler metrics in $c_1\left(L\right)$ and its automorphism group $\mathrm{Aut}(V,L)$ is discrete, $(V,L)$ is asymptotically Chow stable. In this paper, we shall show an example which implies that the above result does not hold in the case where $\mathrm{Aut}(V,L)$ is not discrete.