We demonstrate a simple, general purpose method to cool neutral atoms. A sample containing 3x10(8) cesium atoms prepared in a magneto-optical trap is cooled and simultaneously spin polarized in 10 ms at a density of 1.1x10(11) cm (-3) to a phase space density nlambda(3)(dB) = 1/500, which is almost 3 orders of magnitude higher than attainable in free space with optical molasses. The technique is based on 3D degenerate Raman sideband cooling in optical lattices and remains efficient even at densities where the mean lattice site occupation is close to unity.