  We generalize the construction of a moduli space of semistable pairs
parametrizing isomorphism classes of morphisms from a fixed coherent sheaf to
any sheaf with fixed Hilbert polynomial under a notion of stability to the case
of projective Deligne-Mumford stacks. We study the deformation and obstruction
theories of stable pairs, and then prove the existence of virtual fundamental
classes for some cases of dimension two and three. This leads to a definition
of Pandharipande-Thomas invariants on three-dimensional smooth projective
Deligne-Mumford stacks.
