Dimensional crossover to the one-dimensional (1D) state from higher dimensions has been studied for dilute $$^3$$ 3 He fluid adsorbed in 2.4 nm $$^4$$ 4 He-preplated nanochannels, by susceptibility measurements down to 70 mK using 4.29 MHz nuclear magnetic resonance. In nanochannels, since energy states of $$^3$$ 3 He motion perpendicular to the channel axis are discrete, a genuine 1D $$^3$$ 3 He fluid is expected when the Fermi energy is less than the first excitation $$\Delta _{01}$$ Δ 01 for azimuthal motion. The susceptibilities $$\chi $$ χ above 0.3 K show the Curie-law susceptibilities independent of the $$^3$$ 3 He density, which are characteristic of nondegenerate fluid in higher dimensions. With decreasing the temperature, a significant reduction of $$\chi T$$ χ T was observed from about 0.3 K for all $$^3$$ 3 He densities. It is considered to be due to the dimensional crossover below $$\Delta _{01}\sim 0.5$$ Δ 01 ∼ 0.5 K to the 1D $$^3$$ 3 He state in the semi-degenerate regime above the Fermi temperature. In the 1D state at lower temperatures, T-independent $$\chi $$ χ were observed for $$^3$$ 3 He of 0.019 layers below 0.1 K. It suggests that the 1D $$^3$$ 3 He fluid enters the quantum degenerate regime.