The B + → J/ψη K + decay is observed for the first time using proton-proton collision data collected by the LHCb experiment at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to a total integrated luminosity of 9 fb -1 .The branching fraction of this decay is measured relative to the known branching fraction of the B + → ψ(2S)K + decays and found to bewhere the first uncertainty is statistical, the second is systematic and the third is related to external branching fractions.A first look at the J/ψη mass distribution is performed and no signal of intermediate resonances is observed.