We propose an experimental technique to measure the neutron β-decay lifetime using ultracold neutrons (UCN) produced and stored in a superfluid-4He-filled magnetic trap. UCN will be produced by inelastic scattering of cold (8.9 Å) neutrons in the 4He. The neutron β-decay should result in scintillation that can be detected with high efficiency. This direct measure of the UCN number vs. time can be used to determine the β lifetime. Systematic effects which include leakage of marginally trapped UCN, absorption by impurities (particularly 3He), and inelastic upscattering, are expected to be at the 0.001% level. The expected accuracy based on counting statistics obtainable using existing cold neutron beams is at the 0.004% level.