  The renormalization-scale ($\mu$) dependence of the two-loop inclusive
semileptonic $b\to c\ell^-\bar\nu_\ell$ decay rate is shown to be significant
in the pole mass scheme, and the decay rate is shown to be poorly convergent in
the MS-bar scheme. Three-loop contributions to the decay rate are estimated by
developing Pade approximant techniques particularly suited to perturbative
calculations in the pole mass scheme. An optimized Pade estimate of the
three-loop contributions is obtained by comparison of the Pade estimates with
the three-loop terms determined by renormalization-group invariance. The
resulting three-loop estimate in the pole-mass scheme exhibits minimal
sensitivity to the renormalization scale near $\mu=1.0 GeV$, leading to an
estimated decay rate of $192\pi^3\Gamma(b\to
c\ell^-\bar\nu_\ell)/(G_F^2|V_{cb}|^2)=992\pm 217 GeV^5$ inclusive of
theoretical uncertainties and non-perturbative effects.
