  We compare two associative algebras which encode the "quantum topology" of
Legendrian curves in contact threefolds of product type $S\times\mathbb R$. The
first is the skein algebra of graded Legendrian links and the second is the
Hall algebra of the Fukaya category of $S$. We construct a natural homomorphism
from the former to the latter, which we show is an isomorphism if $S$ is a disk
with marked points and injective if $S$ is the annulus.
