  Let E be a circle bundle over a Riemann surface that supports a contact
structure transverse to the fibers. This paper presents a combinatorial
definition of a differential graded algebra (DGA) that is an invariant of
Legendrian knots in E. The invariant generalizes Chekanov's combinatorial DGA
invariant of Legendrian knots in the standard contact 3-space using ideas from
Eliashberg, Givental, and Hofer's contact homology. The main difficulty lies in
dealing with what are ostensibly 1-parameter families of generators for the
DGA; these are solved using ``Morse-Bott'' techniques. As an application, the
invariant is used to distinguish two Legendrian knots that are smoothly
isotopic, realize a non-trivial homology class, but are not Legendrian
isotopic.
