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We present a measurement of the lepton decay asymmetry Afb in the reaction B̄→D*l-ν̄l using data collected with the CLEO II detector at the Cornell Electron Storage Ring (CESR). The value of Afb confirms that the chirality of the weak interaction is predominantly left-handed in b→c transitions as expected in the standard model, if it is assumed that the lepton current is also left-handed. Using Afb and the previously determined branching ratio, q2 distribution, and D* polarization, we obtain the first measurement of the form-factor ratios that are used to describe this semileptonic decay. © 1993 The American Physical Society.