We present a quenched lattice calculation for the lowest lying <b(b)ov
er bar>g-hybrid states in the framework of NRQCD using the leading ord
er Hamiltonian up to O(m upsilon(2)). We demonstrate the existence of
a nearly degenerate rotational band of states with an excitation energ
y approximately 1.6 GeV above the Y ground state. This lies around the
<B(B)over bar>(j)-threshold, but well above the <B(B)over bar>-thres
hold. Therefore a heavy hybrid signal may well be detected if the cent
er-of-mass energy in B-factories is raised a few hundred MeV to coinci
de with other resonances above the 4S state. Our prediction is consist
ent with most phenomenological models and lattice calculations carried
out in the static limit. [S0556-2821(98)50707-2].