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