  We present a model-independent prediction for $R(\eta_c) \! \equiv \!
\mathcal{BR} (B_c \rightarrow \eta_c \, \tau^+\nu_\tau)/ \mathcal{BR} (B_c
\rightarrow \eta_c \, \mu^+\nu_\mu)$. This prediction is obtained from the form
factors through a combination of dispersive relations, heavy-quark relations at
zero-recoil, and the limited existing determinations from lattice QCD. The
resulting prediction, $R(\eta_c)=0.29(5)$, agrees with the weighted average of
previous model predictions, but with reduced uncertainties.
