Abstract: The B+ -> J psi eta'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 13TeV, 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+ -> psi(2S)K+ decay and found to be B(B+ -> J psi eta'K+)/B(B+ -> psi(2S)K+) = (4.91 +/- 0.47 +/- 0.29 +/- 0.07) x 10(-2), where the first uncertainty is statistical, the second is systematic and the third is related to external branching fractions. A first look at the J/psi eta' mass distribution is performed and no signal of intermediate resonances is observed.