  There are five maximally supersymmetric backgrounds in four-dimensional
off-shell N=1 supergravity, two of which are well known: Minkowski superspace
M^{4|4} and anti-de Sitter superspace AdS^{4|4}. The three remaining
supermanifolds support spacetimes of different topology, which are: R x S^3,
AdS_3 x R, and a supersymmetric plane wave isometric to the Nappi-Witten group.
As is well known, the Minkowski and anti-de Sitter superspaces are solutions of
the Poincar\'e and anti-de Sitter supergravity theories, respectively. Here we
demonstrate that the other three superspaces are solutions of no-scale $R^2$
supergravity. We also present a new (probably the simplest) derivation of the
maximally supersymmetric backgrounds of off-shell N=1 supergravity.
