  Line intensity mapping (LIM) has the potential to produce highly precise
measurements of scale-dependence bias from primordial non-Gaussianity (PNG) due
to its ability to map much larger volumes than are available from galaxy
surveys. PNG parameterized by $f_{NL}$ leads to a scale-dependent correction to
the bias, and therefore a correction to the line intensity power spectrum.
However, LIM experiences contamination from foreground emission, including
interloping emission lines from other redshifts which alter the power spectra
of the maps at these scales, potentially biasing measurements of $f_{NL}$. Here
we model the effect of line interlopers on upcoming line intensity mapping
probes of primordial non-Gaussianity (PNG) from inflation. As an example, we
consider the $[\rm CII]$ line at target redshift $z_t = 3.6$ to probe PNG, with
the important systematic concern being foreground contamination from CO lines
residing at redshifts different from the target redshift. We find interloper
lines can lead to a significant bias and an increase in errors for our PNG
constraints, leading to a false positive for non-standard inflation models. We
model how well the cross-correlation technique could reduce this interloper
contamination. We find the uncertainty of $f_{NL}$ reduces by factors of two
and six for local and orthogonal shape PNG respectively, and by a factor of
five for local shape if we consider seven interloper lines, almost eliminating
the effect of interlopers. This work shows that using cross-power and
auto-power spectra of line intensity maps jointly could potentially remove the
effects of interlopers when measuring non-Gaussianity.
