We demonstrate sub-Doppler laser cooling of ^{39} K using degenerate Raman sideband cooling via the 4S _{1/2} \rightarrow 5P _{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} atoms cooled down to a sub-Doppler temperature of 4 \upmu K, reaching a peak density of 3.9 \times 10^{9} atoms/cm ^{3} , a phase-space density greater than 10^{-5} , and an average vibrational level of \langle \nu \rangle=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.