We demonstrate sub-Doppler laser cooling of ^{39}39K using degenerate Raman sideband cooling via the 4S_{1/2} \rightarrow1/2→5P_{1/2}1/2 transition at 404.8 nm. By using an optical lattice in combination with a magnetic field and optical pumping beams, we obtain a spin-polarized sample of up to 5.6 \times 10^{7}5.6×107 atoms cooled down to a sub-Doppler temperature of 4 \upmuμK, reaching a peak density of 3.9 \times 10^{9}3.9×109 atoms/cm^{3}3, a phase-space density greater than 10^{-5}10−5, and an average vibrational level of \langle \nu \rangle=0.6⟨ν⟩=0.6 in the lattice. This work opens up the possibility of implementing a single-site imaging scheme in a far-detuned optical lattice utilizing shorter wavelength transitions in alkali atoms, thus allowing improved spatial resolution.