We have developed a neutron source based on the ⁷Li(p,n) reaction using the high-intensity  Soreq Applied Research Accelerator Facility (SARAF) and a Liquid-Lithium Target (LiLiT). The proton beam (1-2 mA, 1.91 MeV), just above the reaction energy threshold, is incident on a free-surface liquid-lithium jet (~ 200^oC) flowing at high velocity and produces neutrons within ~ 4 microns of the jet surface. The proton beam is stopped in the lithium jet (1.5 mm thick) and the beam power of several kW is transported to a heat exchanger. The SARAF-LiLiT setup was recently commissioned and produces a forward-directed neutron beam in the 10¹⁰ n/s range peaked at an energy of ~30 keV, the highest-intensity source of this type presently available. The neutron source is used in nuclear astrophysics experiments to study neutron-induced nucleosynthesis reactions and constitutes a breakthrough towards production of accelerator-based neutrons for Boron Neutron Capture Therapy (BNCT).