We present a quenched lattice calculation for the lowest lying $b bar b g$-hybrid states in the framework of NRQCD using the leading order Hamiltonian up to ${cal O}(mv^2)$. We demonstrate the existence of a nearly degenerate rotational band of states with an excitation energy approximately 1.6 GeV above the $Upsilon$ ground state. This lies around the $B bar B_J^*$-threshold but well above the $B bar B$-threshold. Therefore a heavy hybrid signal may well be detected if the centre-of-mass energy in B-factories is raised a few hundred MeV to coincide with other resonances above the 4S state. Our prediction is consistent with most phenomenological models and lattice calculations carried out in the static limit.
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