Pulsed NMR techniques have been used to study the dynamics of 3 He confined to the interior of the hexagonal nanochannels of MCM-41 for which the walls were coated with a monolayer of 4He as determined by isotherm measurements. The 3 He was added afterward to form a 1D 3He line density of about 0.1 A-1, corresponding to a Fermi temperature of T F 120 mK. A distinct and appreciable departure from the Curie law was observed for the nuclear spin magnetization below 0.5 K. The temperature dependence of the nuclear spin-lattice relaxation times, T 1, for temperatures 0.05 < T < 2.5 K, followed the expected linear behavior at low temperatures, and a peak was observed at T 2T F consistent with the Luttinger liquid theory as predicted by Polini et al. (Phys Rev Lett 98:266403, 2007). The observed temperature dependence of the nuclear spin-spin relaxation times, T 2, differed considerably from that observed for T 1, with a minimum at T = 0.8 K, similar to the tendency reported by Matsushita and colleagues.