We develop a topological vertex formalism for computing the Donaldson-Thomas invariants of Calabi-Yau orbifolds. The basic combinatorial object is the orbifold vertex VλμνG, a generating function for the number of 3D partitions asymptotic to 2D partitions λ, μ, ν and colored by representations of a finite Abelian group G acting on C3. In the case where G?Zn acting on C3 with transverse A_(n-1) quotient singularities, we give an explicit formula for VλμνG in terms of Schur functions. We discuss applications of our formalism to the Donaldson-Thomas crepant resolution conjecture and to the orbifold Donaldson-Thomas/Gromov-Witten correspondence. We also explicitly compute the Donaldson-Thomas partition function for some simple orbifold geometries: the local football Pa,b1 and the local BZ2 gerbe.
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