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We examine the Wess-Zumino-Novikov-Witten (WZNW) model on a circle andcompute the Poisson bracket algebra for left and right moving chiral groupelements. Our computations apply for arbitrary groups and boundary conditions,the latter being characterized by the monodromy matrix. Unlike in previoustreatments, they do not require specifying a particular parametrization of thegroup valued fields in terms of angles spanning the group. We do however findit necessary to make a gauge choice, as the chiral group elements are not gaugeinvariant observables. (On the other hand, the quadratic form of the Poissonbrackets may be defined independent of a gauge fixing.) Gauge invariantobservables can be formed from the monodromy matrix and these observables areseen to commute in the quantum theory.Comment: 21 page

POISSON BRACKET ALGEBRA FOR CHIRAL GROUP ELEMENTS IN THE WZNW MODEL