We report on measurements of the inclusive production of J, Ψ′ and χc 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 χc mesons are reconstructed via the decay mode χc → J + γ. 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 → χc1 + X) = (2.7 ± 0.6 (stat.) ± 0.5 (sys.)) × 10⁻³. In the absence of a clear χc2 signal, the upper limit at 90% C.L. is set: Br(Z → χc2 + X) < 3.2 × 10⁻³.