We derive the q-deformation of the chiral Gross-Taylor holomorphic string
large N expansion of two dimensional SU(N) Yang-Mills theory. Delta functions
on symmetric group algebras are replaced by the corresponding objects
(canonical trace functions) for Hecke algebras. The role of the Schur-Weyl
duality between unitary groups and symmetric groups is now played by q-deformed
Schur-Weyl duality of quantum groups. The appearance of Euler characters of
configuration spaces of Riemann surfaces in the expansion persists. We discuss
the geometrical meaning of these formulae
