We study the clustering properties of the first galaxies formed in the Universe. We find that, due to chemical enrichment of the inter-stellar medium by isolated Population III stars formed in mini-halos at redshift z>30, the (chronologically) first galaxies are composed of metal-poor Population II stars and are highly clustered on small scales. In contrast, chemically pristine galaxies in halos with mass M~10^8 M_sun may form at z<20 in relatively underdense regions of the Universe. This occurs once self-enrichment by Population III in mini-halos is quenched by the build-up of an $H_2$ photo-dissociating radiative background in the Lyman-Werner bands. We find that these chemically pristine galaxies are spatially uncorrelated. Thus, we expect that deep fields with the James Webb Space Telescope may detect clusters of chemically enriched galaxies but individual chemically pristine objects. We predict that metal-free galaxies at 10 <= z <= 15$ have surface densities of about 80 per square arcmin and per unit redshift but most of them will be too faint even for JWST. However, the predicted density makes these objects interesting targets for searches behind lensing clusters.
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