The Chow ring of Mbar_{0,m}(n, d)

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.