  We study the Chow ring of the moduli stack of prestable curves and define the
notion of tautological classes on this stack. We extend formulas for
intersection products and functoriality of tautological classes under natural
morphisms from the case of the tautological ring of the moduli space of stable
curves. In genus 0, we show that the Chow ring of the stack of prestable curves
coincides with the tautological ring and give a complete description in terms
of (additive) generators and relations. This generalizes earlier results by
Keel and Kontsevich-Manin for the spaces of stable curves. Our argument uses
the boundary stratification of the moduli stack together with the study of the
first higher Chow groups of the strata, in particular providing a new proof of
the results of Kontsevich and Manin.
