  We extend the Fermi gas approach to a class of ABJM-like necklace quiver
theories without parity invariance. The resulting partition function on $S^3$
retains the form of an Airy function, but now includes a phase that scales as
$Nk$ in the large-$N$ limit where $k$ is an overall Chern-Simons level. We
demonstrate the presence of this phase both analytically and numerically in the
case of a three node quiver.
