We report on measurements of the inclusive production of J, ψ and χ c mesons in hadronic Z decays, based on 3.2 million hadronic events collected using the L3 detector at LEP. The J and ψ mesons are reconstructed through their decays into lepton pairs, while the χ c mesons are reconstructed via the decay mode χ c → J + y. The measured branching fractions are: Br(Z → J + X) = (3.40 ± 0.23 (stat.) ± 0.27 (sys.)) 10 - 3 , Br(Z → ψ + X) = (1.6 ± 0.5 (stat.) ± 0.3 (sys.)) 10 - 3 , Br(Z → χ c 1 + X) = (2.7 ± 0.6 (stat.) ± 0.5 (sys.)) 10 - 3 . In the absence of a clear χ c 2 signal, the upper limit at 90% C.L. is set: Br(Z → χ c 2 + X) < 3.2 10 - 3 .