We present a precise measurement of 3 He analyzing powers for p- 3 He elastic scattering with the polarized 3 He target at 50, 65, 70, and 100 MeV. The data at 65 and 70 MeV are compared with the theoretical predictions based on the modern nucleon-nucleon potentials. Large discrepancies between the data and the predictions are clearly seen at the angles where the 3 He analyzing power takes the minimum and maximum values, which are not explained by Δ -isobar effects. [ABSTRACT FROM AUTHOR]