  Generalizing toric varieties, we introduce toric Deligne-Mumford stacks which
correspond to combinatorial data. The main result in this paper is an explicit
calculation of the orbifold Chow ring of a toric Deligne-Mumford stack. As an
application, we prove that the orbifold Chow ring of the toric Deligne-Mumford
stack associated to a simplicial toric variety is a flat deformation of (but is
not necessarily isomorphic to) the Chow ring of a crepant resolution.
