  Using cosmological volume simulations and a custom built sub-grid model for
Pop~III star formation, we examine the baseline dust extinction in the first
galaxies due to Pop~III metal enrichment in the first billion years of cosmic
history. We find that while the most enriched, high-density lines of sight in
primordial galaxies can experience a measurable amount of extinction from
Pop~III dust ($E(B-V)_{\rm max}=0.07,\ A_{\rm V,max}\approx0.28$), the average
extinction is very low with $\left< E(B-V) \right> \lesssim 10^{-3}$. We derive
a power-law relationship between dark matter halo mass and extinction of
$E(B-V)\propto M_{\rm halo}^{0.80}$. Performing a Monte Carlo parameter study,
we establish the baseline reddening of the UV spectra of dwarf galaxies at high
redshift due to Pop~III enrichment only. With this method, we find
$\left<\beta_{\rm UV}\right>-2.51\pm0.07$, which is both nearly halo mass and
redshift independent.
