  For a polarized algebraic manifold $(X,L)$, let $T$ be an algebraic torus in
the group of all holomorphic automorphisms of $X$. Then strong relative
K-stability will be shown to imply asymptotic relative Chow-stability. In
particular, by taking $T$ to be trivial, we see that asymptotic Chow-stability
follows from strong K-stability.
