  We describe the Chow ring with rational coefficients of the moduli space of
stable maps with marked points Mbar_{0,m}(n,d) as the subring of invariants of
a ring B, relative to the action of the group of symmetries of d elements. B is
computed by following a sequence of intermediate spaces for Mbar_{0,m}(n,d) and
relating them to substrata of Mbar_{0,1}(n,d+m-1). An additive basis for the
Chow ring is presented.
