We calculate the polarisation of psi's and UPSILON's produced by the f
ragmentation of heavy quarks. We find that fragmentation to transverse
ly aligned quarkonium is slightly enhanced relative to longitudinally
polarised quarkonium. This net alignment corresponds to a approximatel
y 5% asymmetry in the angular distribution of leptons produced in the
subsequent decay of the quarkonium. We point out that the leading gluo
n contribution to psi and UPSILON production arises from the evolution
of the charm quark fragmentation function, rather than from direct gl
uon fragmentation.