We provide a translation between Chekanov's combinatorial theory for
invariants of Legendrian knots in the standard contact R^3 and a relative
version of Eliashberg and Hofer's Contact Homology. We use this translation to
transport the idea of ``coherent orientations'' from the Contact Homology world
to Chekanov's combinatorial setting. As a result, we obtain a lifting of
Chekanov's differential graded algebra invariant to an algebra over Z[t,t^{-1}]
with a full Z grading.Comment: 32 pages, 17 figures; small technical corrections to proof of Thm 3.7
and example 4.
