  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.
