We report measurements of the inclusive production of heavy quarkonium states in Z decays based on the analysis of 3.6 million hadronic events collected by the L3 detector at LEP. The measurement of inclusive J production and an improved 95% confidence level upper limit on Υ production are presented. In addition, two independent measurements of the ratio, fp , of prompt J mesons to those from B decay are made using two different isolation cuts to separate prompt J mesons from J mesons produced in the decays of b hadrons. The results are: , Br(Z→ϒ(1S)+X)<4.4×10−5, .