  We calculate the Isgur-Wise function by measuring the elastic scattering
amplitude of a $D$ meson in the quenched approximation on a $24^3\times48$
lattice at $\beta=6.2$, using an $O(a)$-improved fermion action. Fitting the
resulting chirally-extrapolated Isgur-Wise function to Stech's
relativistic-oscillator parametrization, we obtain a slope parameter
$\rho^2=1.2+7-3. We then use this result, in conjunction with heavy-quark
symmetry, to extract $V_{cb}$\ from the experimentally measured $\bar B\to
D^*l\bar\nu\,$\ differential decay width. We find
$|V_{cb}|\sqrt{\tau_B/1.48{\mathrm ps}}= 0.038 +2-2 +8-3, where the first set
of errors is due to experimental uncertainties, while the second is due to the
uncertainty in our lattice determination of $\rho^2$.
