  In this note we point out that a symmetric product orbifold CFT can be
twisted by a unique nontrivial two-cocycle of the permutation group. This
discrete torsion changes the spins and statistics of corresponding
second-quantized string theory making it essentially ``supersymmetric.'' The
long strings of even length become fermionic (or ghosts), those of odd length
bosonic. The partition function and elliptic genus can be described by a sum
over stringy spin structures. The usual cubic interaction vertex is odd and
nilpotent, so this construction gives rise to a DLCQ string theory with a
leading quartic interaction.
