We present a nuclear magnetic resonance study of the low-temperature spin-density-wave ͑SDW͒ ground state in the quasi-one-dimensional conductor ͑TMTSF͒ 2 PF 6 ͓bis-͑tetramethyl-tetraselenafulval-ene͒hexafluorophosphate͔. Using magnetic fields up to 22 T, we have measured the 77 Se spin-lattice (T 1 Ϫ1 ) andspin-spin relaxation rates (T 2 Ϫ1 ) above and below the SDW transition (T SDW Ϸ12 K͒. Between T SDW and Ϸ4 K, we observe anomalously fast and Korringa-like T 1 Ϫ1 ; below 4 K, T 1 Ϫ1 decays rapidly. A reduction in T 2 Ϫ1 is also observed at 4 K, but the absorption linewidth does not change to within experimental error. We attribute this behavior to an incomplete SDW transition at T SDW , leaving residual carriers at the Fermi level, and a subsequent consummation of the transition at 4 K. Our data below 4 K are consistent with a simple model of the temperature dependence of T 1 Ϫ1 in a fully gapped and low-dimensional conductor.