  Montonen-Olive duality implies that the categories of A-branes on the moduli
spaces of Higgs bundles on a Riemann surface C for a pair of Langlands-dual
groups are equivalent. We reformulate this as a statement about categories of
B-branes on the quantized moduli spaces of flat connections for these groups.
We show that it implies the statement of the Quantum Geometric Langlands
duality with a purely imaginary ``quantum parameter'' which is proportional to
the inverse of the Planck constant of the gauge theory. The ramified version of
the story is also considered.
