A polarized He3 target, which uses conventional optical pumping with He4 discharge lamps, has been used for the measurement of He3 analyzing powers Ay(θ) at energies of 25.0, 30.0, 32.5, and 35.0 MeV. The statistical uncertainties in the data are on the order of 0.03; the systematic uncertainty is estimated to be 0.05. These data are compared with fits and predictions from various phase shift analyses.@en