  We evaluate the one-loop corrections to the Wilson coefficient of the kinetic
operator in the operator product expansion of the differential B -> X_c l nu
decay rate. With a moderate cut on the lepton energy, the one-loop terms change
the kinetic operator contributions to spectral moments by about 20%. This
amounts to a small correction for leptonic and hadronic moments, except for
those which vanish at the lowest order, where the effect can be sizable.
Together with a two-loop calculation of the leading-power rate and an
evaluation of the one-loop corrections to the Wilson coefficient of the
chromo-magnetic operator, our results will allow for a high-precision
determination of |V_cb| and the b- and c-quark masses.
