  The symplectic and Poisson structures of the Liouville theory are derived
from the symplectic form of the SL(2,R) WZNW theory by gauge invariant
Hamiltonian reduction. Causal non-equal time Poisson brackets for a Liouville
field are presented. Using the symmetries of the Liouville theory, symbols of
chiral fields are constructed and their *-products calculated. Quantum
deformations consistent with the canonical quantisation result, and a non-equal
time commutator is given.
