  A lattice QCD calculation of the $\bar{B}\to Dl\bar{\nu}$ decay form factors
is presented. We obtain the value of the form factor $h_+(w)$ at the
zero-recoil limit $w=1$ with high precision by considering a ratio of
correlation functions in which the bulk of the uncertainties cancels. The other
form factor $h_-(w)$ is calculated, for small recoil momenta, from a similar
ratio. In both cases, the heavy quark mass dependence is observed through
direct calculations with several combinations of initial and final heavy quark
masses. Our results are $h_+(1) = 1.007(6)(2)(3)$ and
$h_-(1)=-0.107(28)(04)(^{10}_{30})$. For both the first error is statistical,
the second stems from the uncertainty in adjusting the heavy quark masses, and
the last from omitted radiative corrections. Combining these results, we obtain
a precise determination of the physical combination $F_{B\to
D}(1)=1.058(^{20}_{17})$, where the mentioned systematic errors are added in
quadrature. The dependence on lattice spacing and the effect of quenching are
not yet included, but with our method they should be a fraction of $F_{B\to
D}-1$.
