(B)over-bar → D*l(ν)over-bar form factor at zero recoil from three-flavor lattice QCD: A model independent determination of |Vcb|

We present the first lattice QCD calculation of the form factor for (B) over bar -> D*l (v) over bar with three flavors of sea quarks. We use an improved staggered action for the light valence and sea quarks ( the MILC configurations), and the Fermilab action for the heavy quarks. The form factor is computed at zero recoil using a new double ratio method that yields the form factor more directly than the previous Fermilab method. Other improvements over the previous calculation include the use of much lighter light-quark masses, and the use of lattice ( staggered) chiral perturbation theory in order to control the light-quark discretization errors and chiral extrapolation. We obtain for the form factor, F-B -> D* (1) = 0. 921(13)(20), where the first error is statistical and the second is the sum of all systematic errors in quadrature. Applying a 0.7% electromagnetic correction and taking the latest PDG average for F-B -> D* (1)vertical bar V-cb vertical bar leads to vertical bar V-cb vertical bar = (38. 7 +/- 0.9(exp) +/- 1.0(theo)) X 10(-3).