  We put forward a unimodular $N=1, d=4$ anti-de Sitter supergravity theory off
shell. This theory, where the Cosmological Constant does not couple to gravity,
has a unique maximally supersymmetric classical vacuum which is Anti-de Sitter
spacetime with radius given by the equation of motion of the auxiliary scalar
field, ie, $S=\frac{3}{\kappa L}$. However, we see that the non-supersymmetric
classical vacua of the unimodular theory are Minkowski and de Sitter spacetimes
as well as anti-de Sitter spacetime with radius $l\neq L$.
