Large parity violating longitudinal single spin asymmetries A^{e^-}_L= -0.86^{+0.14}_{-0.30} and A^{e^+}_L= 0.88^{+0.12}_{-0.71} are observed for inclusive high transverse momentum electrons and positrons in polarized pp collisions at a center of mass energy of sqrt{s}=500 GeV with the PHENIX detector at RHIC. These e^{+/-} come mainly from the decay of W^{+/-} and Z^0 bosons, and the asymmetries directly demonstrate parity violation in the couplings of the W^{pm} to the light quarks. The observed electron and positron yields were used to estimate W^pm boson production cross sections equal to sigma(pp to W^+ X) times BR(W^ to u_e)= 144.1+/-21.2(stat)^{+3.4}_{-10.3}(syst) +/- 15%(norm) pb, and sigma(pp to W^{-}X) times BR(W^to e^-bar{ u_e}) = 31.7+/-12.1(stat)^{+10.1}_{-8.2}(syst)+/-15%(norm) pb.
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