A search is performed for pair-produced spin-3/2 excited top quarks ((t∗\overline{t}∗)), each decaying to a top quark and a gluon. The search uses data collected with the CMS detector from pp collisions at a center-of-mass energy of (\sqrt{s})=8TeV, selecting events that have a single isolated muon or electron, an imbalance in transverse momentum, and at least six jets, of which one must be compatible with originating from the fragmentation of a b quark. The data, corresponding to an integrated luminosity of 19.5 fb⁻¹, show no significant excess over standard model predictions, and provide a lower limit of 803 GeV at 95% confidence on the mass of the spin-3/2 t * quark in an extension of the Randall-Sundrum model, assuming a 100% branching fraction of its decay into a top quark and a gluon. This is the first search for a spin-3/2 excited top quark performed at the LHC.