We report on the realization of sub-Doppler laser cooling of sodium atoms in gray molasses using the D1 optical transition ($3s, ^2S_{1/2} rightarrow 3p, ^2P_{1/2}$) at 589.8 nm. The technique is applied to samples containing $3times10^9$ atoms, previously cooled to 350 $mu$K in a magneto-optical trap, and it leads to temperatures as low as 9 $mu$K and phase-space densities in the range of $10^{-4}$. The capture efficiency of the gray molasses is larger than 2/3, and we observe no density-dependent heating for densities up to $10^{11}$ cm$^{-3}$.
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