We report new limits on right-handed currents, based on precise measurement of the endpoint of the e spectrum from .mu. decay. Highly polarized .mu. from the TRIUMF surface beam were stopped in pure metal foils within either an 1.1-T spin-holding longitudinal field, or a 70-gauss spin-precessing transverse field. Decay e+ emitted within 200 mrad of the beam direction were momentum-analyzed to +-0.2%. For the spin-held data, decay via (V-A) currents requires the e+ rate to approach zero in the beam direction at the endpoint. Measurement of this rate sets the 90% confidence limits xi P/sub .mu.[delta]rho> 0.9959 and M(W/sub R/)> 380 GeV, where W/sub R/ is the possible right-handed gauge boson. For the spin-precessed data we independently determine a 90% confidence limit xi P/sub .mu./delta/rho> 0.9918. 18 references.