  While the ABJ Chern-Simons-matter theory and its string theory dual
manifestly lack parity invariance, no sign of parity violation has so far been
observed on the weak coupling spin chain side. In particular, the planar
two-loop dilatation generator of ABJ theory is parity invariant. In this letter
we derive the non-planar part of the two-loop dilatation generator of ABJ
theory in its SU(2)xSU(2) sub-sector. Applying the dilatation generator to
short operators, we explicitly demonstrate that, for operators carrying
excitations on both spin chains, the non-planar part breaks parity invariance.
For operators with only one type of excitation, however, parity remains
conserved at the non-planar level. We furthermore observe that, as for ABJM
theory, the degeneracy between planar parity pairs is lifted when non-planar
corrections are taken into account.
