New electron scattering measurements have been made that extend data on the 3He elastic magnetic form factor up to Q2 = 42.6fm-2. These new data test theoretical conjectures regarding non-nucleonic effects in the three-body system. The very small cross sections, as low as 10-40cm2/sr, required the use of a high-pressure cryogenic gas target and a detector system with excellent background rejection capability. No existing theoretical calculation satisfactorily accounts for all the available data.