We present a measurement of the polarization observed for bottomonium state
s produced in p-Cu collisions at roots = 38.8 GeV. The angular distribution
of the decay dimuons of the Y (1S) state shows no polarization at small va
lues of the fractional longitudinal momentum chi (F) add transverse momentu
m p(T) but significant positive transverse production polarization for eith
er p(T) > 1.8 GeV/c or for chi (F) > 0.35. The Y (2S + 3S) (unresolved) sta
tes show a large transverse production polarization at all values of chi (F
) and pr measured. These observations challenge NRQCD calculations of the p
olarization expected in the hadronic production of bottomonium states.