  In this article, we calculate the $B_c^* \to \eta_c$ form-factors with the
three-point QCD sum rules, then study the semileptonic decays $B_c^* \to \eta_c
\ell \bar{\nu}_{\ell}$. The tiny decay widths may be observed experimentally in
the future at the LHCb, while the $B_c^* \to \eta_c$ form-factors can be taken
as basic input parameters in other phenomenological analysis.
