  We define a differential graded algebra associated to Legendrian knots in
Seifert fibered spaces with transverse contact structures. This construction is
distinguished from other combinatorial realizations of contact homology
invariants by the existence of orbifold points in the Reeb orbit space of the
contact manifold. These orbifold points are images of the exceptional fibers of
the Seifert fibered manifold, and they play a key role in the definitions of
the differential and the grading, as well as the proof of invariance. We apply
the invariant to distinguish Legendrian knots whose homology is torsion and
whose underlying topological knot types are isotopic; such examples exist in
any sufficiently complicated contact Seifert fibered space.
