We have performed thermodynamic and NMR relaxation time measurements of He-3 adsorbed in the pores of the mesoporous molecular sieve MCM-41 at temperatures down to 1.7 K and at a range of frequencies up to 240 kHz. The MCM-41 substrate comprises a uniform array of quasi-1D straight pores with a diameter of 2.3 nm. We preplated the pores with a monolayer of He-4 to achieve an effective diameter of 1.6 nm at low temperatures. We made NMR measurements as a function of line density and frequency to investigate the spin dynamics and the effect of dimensionality. We observed T-1 proportional to omega(1/2), which is characteristic of one-dimensional diffusion. At these temperatures this arises from a classical size effect in the narrow pores. Our results demonstrate the possibility to study the spin dynamics of a 1D Tomonaga-Luttinger liquid at lower temperatures, where the He-3 liquid will constitute a quantum 1D system.