We have used the narrow 2S1/2→3P3/2 transition in the ultraviolet (uv) to laser cool and magneto-optically trap (MOT) 6Li atoms. Laser cooling of lithium is usually performed on the 2S1/2→2P3/2 (D2) transition, and temperatures of ∼300 μK are typically achieved. The linewidth of the uv transition is seven times narrower than the D2 line, resulting in lower laser cooling temperatures. We demonstrate that a MOT operating on the uv transition reaches temperatures as low as 59 μK. Furthermore, we find that the light shift of the uv transition in an optical dipole trap at 1070 nm is small and blueshifted, facilitating efficient loading from the uv MOT. Evaporative cooling of a two spin-state mixture of 6Li in the optical trap produces a quantum degenerate Fermi gas with 3×10˄6 atoms in a total cycle time of only 11 s.