The technique of adiabatic fast passage has been used to measure the nuclear susceptibility of liquid He3. Measurements along the vaporization curve from 1.2°K to 2.1°K indicate that anti-parallel alignment of the He3 spin system in this temperature range is more important than suggested by previous measurements. Unless existing data at temperatures below 1°K are incorrect, it appears that the susceptibility of He3 is not given precisely by the ideal Fermi-Dirac expression. A He3 cryostat has been constructed to extend the measurements to lower temperatures. Both the operating characteristics of a preliminary cryostat and the design of the final cryostat are discussed.