We report on a study of heavy quark bound states containing an additional excitation of the gluonic degrees of freedom. To this end we employ the nonrelativistic QCD approach on coarse and asymmetric lattices, where we discard vacuum polarization effects and neglect all spin-correction terms. We find a clear hybrid signal on all our lattices ( as = 0.15,…,0.47 fm). We have studied in detail the lattice spacing artifacts, finite volume effects, and mass dependence. Within the above approximations we predict the lowest lying hybrid excitation in charmonium to be 1.323(13) GeV above the ground state, where we use the 1P-1S splitting to set the scale. The bottomonium hybrid was found to be 1.542(8) GeV above its ground state.