Examples are given of prime Legendrian knots in the standard contact 3–space
that have arbitrarily many distinct Chekanov polynomials, refuting a conjecture
of Lenny Ng. These are constructed using a new “Legendrian tangle replace-
ment” technique. This technique is then used to show that the phenomenon
of multiple Chekanov polynomials is in fact quite common. Finally, building
on unpublished work of Yufa and Branson, a tabulation is given of Legendrian
fronts, along with their Chekanov polynomials, representing maximal Thurston–
Bennequin Legendrian knots for each knot type of nine or fewer crossings. These
knots are paired so that the front for the mirror of any knot is obtained in a
standard way by rotating the front for the knot