The polarization of inclusive Y(nS) at the Fermilab Tevatron is calculated
within the nonrelativistic QCD factorization framework. We use a recent det
ermination of the NRQCD matrix elements from fitting the CDF data on bottom
onium production from run IB of the Tevatron. The result for the polarizati
on of Y(1S) integrated over the transverse momentum bin 8<(pT)<20 GeV is co
nsistent with a recent measurement by the CDF Collaboration. The transverse
polarization of Y(IS) is predicted to increase steadily for p(T) greater t
han about 10 GeV. The Y(2S) and Y(3S) are predicted to have significantly l
arger transverse polarizations than Y(1S).