  Ultracold polar molecules offer strong electric dipole moments and rich
internal structure, which makes them ideal building blocks to explore exotic
quantum matter, implement novel quantum information schemes, or test
fundamental symmetries of nature. Realizing their full potential requires
cooling interacting molecular gases deeply into the quantum degenerate regime.
However, the complexity of molecules which makes their collisions intrinsically
unstable at the short range, even for nonreactive molecules, has so far
prevented the cooling to quantum degeneracy in three dimensions. Here, we
demonstrate evaporative cooling of a three-dimensional gas of fermionic
sodium-potassium molecules to well below the Fermi temperature using microwave
shielding. The molecules are protected from reaching short range with a
repulsive barrier engineered by coupling rotational states with a blue-detuned
circularly polarized microwave. The microwave dressing induces strong tunable
dipolar interactions between the molecules, leading to high elastic collision
rates that can exceed the inelastic ones by at least a factor of 460. This
large elastic-to-inelastic collision ratio allows us to cool the molecular gas
down to 21 nanokelvin, corresponding to 0.36 times the Fermi temperature. Such
unprecedentedly cold and dense samples of polar molecules open the path to the
exploration of novel many-body phenomena, such as the long-sought topological
p-wave superfluid states of ultracold matter.
