  We develop a new method in lattice QCD to calculate the form factor F(1) at
zero recoil. This is the main theoretical ingredient needed to determine
|V(cb)| from the exclusive decay anti-B --> D* lepton anti-neutrino. We
introduce three ratios, in which most of statistical and systematic error
cancels, making a precise calculation possible. We fit the heavy-quark mass
dependence directly, and extract the 1/m_Q^2 and three of the four 1/m_Q^3
corrections in the heavy-quark expansion. In this paper we show how the method
works in the quenched approximation, obtaining F(1) = 0.913
(+0.024-0.017)(+/-0.016)(+0.003-0.014)(+0.000-0.016)(+0.006-0.014) where the
uncertainties come, respectively, from statistics and fitting, matching lattice
gauge theory to QCD, lattice spacing dependence, light quark mass effects, and
the quenched approximation. We also discuss how to reduce these uncertainties
and, thus, to obtain a model-independent determination of |V(cb)|.
