A new invariant of Legendrian knots will be defined, taking values in the knot Floer homology of the underlying null-homologous knot. With the aid of this invariant we find transversely non-simple knots in many overtwisted contact structures, and show that the Eliashberg-Chekanov twist knots (in particular the $7_2$ knot in Rolfsen's table) are not transversely simple.