  In this article, we explore a polynomial invariant for Legendrian knots which
is a natural extension of Jones polynomial for (topological) knots. To this
end, a new type of skein relation is introduced for the front projections of
Legendrian knots. Further, we give a categorification of the polynomial
invariant for Legendrian knots which is a natural extension of Khovanov
homology for knots. The Thurston-Bennequin invariant of Legendrian knot appears
naturally in the construction of the homology as the grade-shift. The
constructions of the polynomial invariant and its categorification are natural
in the sense that if we treat Legendrian knots as only knots (that is, we
forget the geometry on the knots), then we recover the Jones polynomial and
Khovanov homology respectively. In the end, we discuss strengths and
limitations of these invariants.
