  For a Legendrian knot L in R^3 with a chosen Morse complex sequence (MCS) we
construct a differential graded algebra (DGA) whose differential counts "chord
paths" in the front projection of L. The definition of the DGA is motivated by
considering Morse-theoretic data from generating families. In particular, when
the MCS arises from a generating family we give a geometric interpretation of
our chord paths as certain broken gradient trajectories which we call "gradient
staircases". Given two equivalent MCS's we prove the corresponding linearized
complexes of the DGA are isomorphic. If the MCS has a standard form, then we
show that our DGA agrees with the Chekanov-Eliashberg DGA after changing
coordinates by an augmentation.
