In decays of the Z^0, the dominant mechanism for the direct production of charmonium states is the decay of the Z^0 into a charm quark or antiquark followed by its fragmentation into the charmonium state. We calculate the fragmentation functions describing the splitting of charm quarks into S-wave charmonium states to leading order in the QCD coupling constant. Leading logarithms of M_Z/m_c are summed up using Altarelli-Parisi evolution equations. Our analytic result agrees with the complete

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... ding order calculation of the rate for Z^0 →ψ c c̅. We also use our fragmentation functions to calculate the production rate of heavy quarkonium states in W^±, top quark, and Higgs decays.