  We present a model-independent bound on $R(J/\psi) \! \equiv \! \mathcal{BR}
(B_c^+ \rightarrow J/\psi \, \tau^+\nu_\tau)/ \mathcal{BR} (B_c^+ \rightarrow
J/\psi \, \mu^+\nu_\mu)$. This bound is constructed by constraining 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 95\% confidence-level bound, $0.20\leq R(J/\psi)\leq0.39$, agrees
with the recent LHCb result at $1.3 \, \sigma$, and rules out some previously
suggested model form factors.
