  We calculate the polarisation of $\psi$'s and $\Upsilon$'s produced by the
fragmentation of heavy quarks. We find that fragmentation to transversely
aligned quarkonium is slightly enhanced relative to longitudinally polarised.
This net alignment corresponds to a $\sim 5\%$ asymmetry in the angular
distribution of leptons produced in the subsequent decay of the quarkonium. We
point out that the leading gluon contribution to $\psi$ and $\Upsilon$
production arises from the evolution of the charm quark fragmentation function,
rather than from direct gluon fragmentation.
