A measurement is reported of the ratio of branching fractions R ( J / ψ ) = B ( B + c → J / ψ τ + ν τ ) / B ( B + c → J / ψ μ + ν μ ) , where the τ + lepton is identified in the decay mode τ + → μ + ν μ ¯ ν τ . This analysis uses a sample of proton-proton collision data corresponding to 3.0     fb − 1 of integrated luminosity recorded with the LHCb experiment at center-of-mass energies of 7 and 8 TeV. A signal is found for the decay B + c → J / ψ τ + ν τ at a significance of 3 standard deviations corrected for systematic uncertainty, and the ratio of the branching fractions is measured to be R ( J / ψ ) = 0.71 ± 0.17 ( stat ) ± 0.18 ( syst ) . This result lies within 2 standard deviations above the range of central values currently predicted by the standard model.