Primordial non-Gaussianity is an invaluable window into the physical processes that gave rise to the cosmological structure. The presence of local shape PNG imprints a distinct scale-dependent correction to the bias of dark matter tracers on large scales, which can be effectively probed via the technique of intensity mapping. Considering an upcoming generation of experiments, we demonstrate that intensity mapping of CO and [CII] emission can improve upon the current best constraints from the {\it Planck} satellite. We show that measurement of the CO intensity power spectrum by a hypothetical next stage of the ground-based COMAP experiment can achieve $\sigma (fNLloc)=3.4$, and that the proposed CMB satellite mission PIXIE can achieve $\sigma (fNLloc)=3.9$ via measurement of [CII] intensity power spectrum.