  We classify closed, conformally flat Lorentzian manifolds of dimension $n
\geq 3$ with unipotent holonomy in PO(2,n). They are all Kleinian and fall into
four different geometric types according to the intersection of the image of
the developing map with a holonomy-invariant isotropic flag. They are
homeomorphic to $S^{n-1} \times S^1$ or a nilmanifold of degree at most three,
up to a finite cover. We classify those admitting an essential conformal flow;
these fall into two geometric types, both homeomorphic to $S^{n-1} \times S^1$
up to finite cover.
