[en] Using the ARGUS detector at the e⁺e^- storage ring DORIS II, we have measured the average polarization of D^*+ mesons originating from exclusive decays anti B⁰ → D^*+l^-anti ν. By comparing the D^*+ decay angular distribution to a functional form 1+αcos²θ, we determine α to be α = 0.7±0.9. This value of α leads to a ratio of longitudinal to transverse decay width Γ_L/Γ_T = 0.85±0.45, which allows the determination, vertical strokeV_cbvertical stroke=0.052±0.011. The importance of the transverse helicity component is manifested in the q² and lepton spectra, which are also presented. (orig.)