The decay Z → Q+ ll, where Q is a J = 1 quarkonium state, has a very clean final state, which should make it easy to detect. The branching ratio of this mode is greater than 10 for ρ, φ, and ψ, indicating that these processes may be detectable at LEP. Well over one million Z decay events have been accumulated at LEP, and further improvements are expected. This makes it possible to investigate r...