  We study vacuum domain walls in a class of four-dimensional $N=1$
supergravity theories where along with the matter field, forming the wall,
there is more than one ``dilaton'', each respecting $SU(1,1)$ symmetry in their
sub-sector. We find {\it supersymmetric} (planar, static) walls, interpolaing
between Minkowski vacuum and a new class of supersymmetric vacua which have a
naked (planar) singularity. Such walls provide the first example of
supersymmetric classical ``solitons'' with naked singularities, and thus
violate the (strong) cosmic censorship conjecture within a supersymmetric
theory.
