Abstract: The B+ -> D*K--(+)pi(+) decay potentially provides an excellent way to investigate charm meson spectroscopy. The decay is searched for in a sample of proton-proton collision data collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3 fb(-1). A clear signal is observed, and the ratio of its branching fraction to that of the B+ -> D*(-)pi(+)pi(+) normalization channel is measured to be beta(B+ -> D*K--(+)pi(+))/beta(B+ -> D*(-)pi(+)pi(+)) = (6.39 +/- 0.27 +/- 0.48) x 10(-2); where the first uncertainty is statistical and the second is systematic. This is the first observation of the B+ -> D*K--(+)pi(+) decay.