  We present a conformal field theory which desribes a homogeneous four
dimensional Lorentz-signature space-time. The model is an ungauged WZW model
based on a central extension of the Poincar\'e algebra. The central charge of
this theory is exactly four, just like four dimensional Minkowski space. The
model can be interpreted as a four dimensional monochromatic plane wave. As
there are three commuting isometries, other interesting geometries are expected
to emerge via $O(3,3)$ duality.
