  The decay rates for the exclusive B decays $B \rightarrow K \eta_c $ and $B
\rightarrow K^* \eta_c$ are calculated in the context of the heavy quark
effective theory. We obtain $\Gamma (B \rightarrow K \eta_c )/\Gamma
(B\rightarrow K\psi )=1.6 \pm 0.2$ and $\Gamma (B\rightarrow K^*\eta_c)/\Gamma
(B \rightarrow K^*\psi )=0.39 \pm 0.04$. These results lead to estimates $BR(B
\rightarrow K \eta_c)=(0.11 \pm 0.02) \% $ and $BR(B \rightarrow K^* \eta_c)=
(0.05 \pm 0.01) \% $ if we use the central current experimental values for
$B\rightarrow (K,K^*)\psi $ branching ratios.
