A pair of conformal sigma-models related by Poisson-Lie T-duality is c
onstructed by starting with the O(2,2) Drinfeld double. The duality re
lates the standard SL(2, R) WZNW model to a constrained sigma-model de
fined on the SL(2, R) group space. The quantum equivalence of the mode
ls is established by using a path integral argument.