New electron scattering measurements have been made that extend data on the (3)He elastic magnetic form factor up to Q(2) = 42.6 fm(-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(-40) cm(2)/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.