A novel technique has been employed to measure the temperature dependence of charge mobilities in liquid 3He under low pressure for 0.25 K < T < 2.0 K. The measurements were made by investigating space-charge-limited currents injected into the liquid from a discharge initiated at a fine metal point by field emission/ionization. The experimental data show less scatter than those obtained previously using conventional methods. The advantages and disadvantages of the space-charge technique, and the feasibility of its use in the millikelvin temperature range, are discussed.