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Primordial non-Gaussianities provide an important test of inflationary models. Although the Planck CMB experiment has produced strong limits on non-Gaussianity on scales of clusters, there is still room for considerable non-Gaussianity on galactic scales. We have tested the effect of local non-Gaussianity on the high redshift galaxy population by running five cosmological N-body simulations down to z=6.5. For these simulations, we adopt the same initial phases, and either Gaussian or scale-dependent non-Gaussian primordial fluctuations, all consistent with the constraints set by Planck on clusters scales. We then assign stellar masses to each halo using the halo - stellar mass empirical relation of Behroozi et al. (2013). Our simulations with non-Gaussian initial conditions produce halo mass functions that show clear departures from those obtained from the analogous simulations with Gaussian initial conditions at z>~10. We observe a >0.3 dex enhancement of the low-end of the halo mass function, which leads to a similar effect on the galaxy stellar mass function, which should be testable with future galaxy surveys at z>10. As cosmic reionization is thought to be driven by dwarf galaxies at high redshift, our findings may have implications for the reionization history of the Universe., 6 pages, 3 figures, 1 table, MNRAS (Letters) in press