The high-field magnetization process of a one-dimensional S = 1/2 trimer system, 3CuCl2 . 2dioxane, is studied on powder samples using a pulse magnet up to 30 T between 1.5 K and 9 K. The magnetization increases nonlinearly and saturates around 15 T, characteristic of low-dimensional Heisenberg antiferromagnets. The magnetization data are consistent with a previously proposed model in which ferromagnetic trimers composed of three S = 1/2 spins are weakly coupled antiferromagnetically to form a S = 3/2 antiferromagnetic chain. Based on this model, the antiferromagnetic intertrimer interaction is directly derived as J(AF) = -16.2 K. However, the observed magnetization curve suggests that a composite spin system consisting of three S = 1/2 spins has more of a quantum nature than does a genuine S = 3/2 system, because the ferromagnetic intratrimer interaction is not sufficiently strong.