We have measured the ratio of prompt production rates of the charmonium states chi(c1) and chi(c2) in 110 pb(-1) of pp collisions at sqrt[s] = 1.8 TeV. The photon from their decay into J/psi(gamma) is reconstructed through conversion into e+e- pairs. The energy resolution this technique provides makes the resolution of the two states possible. We find the ratio of production cross sections sigma(chi(c2))/sigma(chi(c1)) = 0.96+/-0.27(stat)+/-0.11(syst) for events with pT(J/psi) > 4.0 GeV/c, /eta(J/psi)/ < 0.6, and pT(gamma) > 1.0 GeV/c.
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