  In 1980, I. Morrison proved that slope stability of a vector bundle of rank 2
over a compact Riemann surface implies Chow stability of the projectivization
of the bundle with respect to certain polarizations. Using the notion of
balanced metrics and recent work of Donaldson, Wang, and Phong-Sturm, we show
that the statement holds for higher rank vector bundles over compact algebraic
manifolds of arbitrary dimension that admit constant scalar curvature metric
and have discrete automorphism group.
