  We derive a generalization of the classical dynamical Yang-Baxter equation
(CDYBE) on a self-dual Lie algebra $\cal G$ by replacing the cotangent bundle
T^*G in a geometric interpretation of this equation by its Poisson-Lie (PL)
analogue associated with a factorizable constant r-matrix on $\cal G$. The
resulting PL-CDYBE, with variables in the Lie group G equipped with the
Semenov-Tian-Shansky Poisson bracket based on the constant r-matrix, coincides
with an equation that appeared in an earlier study of PL symmetries in the WZNW
model. In addition to its new group theoretic interpretation, we present a
self-contained analysis of those solutions of the PL-CDYBE that were found in
the WZNW context and characterize them by means of a uniqueness result under a
certain analyticity assumption.
