  We compute a time-dependent noncommutativity parameter in a model with a
time-dependent background, a space-time metric of the plane wave type supported
by a Neveu-Schwarz two-form potential. This model is an open string version of
the WZW model based on a non-semi-simple group previously studied by Nappi and
Witten. The background we study is not conformally invariant. We consider a
light-cone action for the sigma-model, compute the worldsheet propagator, and
use it to derive a time-dependent noncommutativity parameter.
