The recoil proton polarization has been measured in the p(e-->,e'p-->)pi(0) reaction in parallel kinematics around W = 1232 MeV, Q2 = 0.121 (GeV/c)2, and epsilon = 0.718 using the polarized cw electron beam of the Mainz Microtron. All three proton polarization components, Px/P(e) = (-11.4+/-1.3+/-1.4)%, P(y) = (-43.1+/-1.3+/-2.2)%, and P(z)/P(e) = (56.2+/-1.5+/-2.6)%, could be measured simultaneously. The Coulomb quadrupole to magnetic dipole ratio, CMR = (-6.4+/-0.7(stat)+/-0.8(syst))%, was determined from Px in the framework of the Mainz Unitary Isobar Model. The consistency among the reduced polarizations and the extraction of the ratio of longitudinal-to-transverse response is discussed.