Given a finite graded poset with labeled Hasse diagram, we construct a
quasi-symmetric generating function for chains whose labels have fixed
descents. This is a common generalization of both Ehrenborg's generating
function for the flag f-vector and a symmetric function associated to a
symmetric labeled posets which arose in the theory of Schubert polynomials.
We show that this construction gives a Hopf morphism from a
reduced incidence Hopf algebra of labeled posets to the algebra of
quasi-symmetric functions.