  Let X be a normal projective variety admitting an action of a semisimple
group with a unique closed orbit. We construct finitely many rational curves in
X, all having a common point, such that every effective one-cycle on X is
rationally equivalent to a unique linear combination of these curves with
non-negative rational coefficients. When X is nonsingular, these curves are
projective lines, and they generate the integral Chow group of one-cycles.
