  We study the large-scale bias parameter of cosmic voids with primordial
non-Gaussian (PNG) initial conditions of the local type. In this scenario, the
dark matter halo bias exhibits a characteristic scale dependence on large
scales, which has been recognized as one of the most promising probes of the
local PNG. Using a suite of $N$-body simulations with Gaussian and non-Gaussian
initial conditions, we find that the void bias features scale-dependent
corrections on large scales, similar to its halo counterpart. We find excellent
agreement between the numerical measurement of the PNG void bias and the
general peak-background split prediction. Contrary to halos, large voids
anti-correlate with the dark matter density field, and the large-scale Gaussian
void bias ranges from positive to negative values depending on void size and
redshift. Thus, the information in the clustering of voids can be complementary
to that of the halos. Using the Fisher matrix formalism for multiple tracers,
we demonstrate that including the scale-dependent bias information from voids,
constraints on the PNG parameter $f_{\rm NL}$ can be tightened by a factor of
two compared to the accessible information from halos alone, when the sampling
density of tracers reaches $4 \times 10^{-3} \, h^3 \mathrm{Mpc}^{-3} $.
