We have measured the ratio of prompt production rates of the charmonium sta
tes chi (c1) and chi (c2) in 110 pb(-1) of p (p) over bar collisions at roo
ts = 1.8 TeV. The photon from their decay into J/Psi gamma is reconstructed
through conversion into ece pairs. The energy resolution this technique pr
ovides makes the resolution of the two states possible. We find the ratio o
f production cross sections sigma chi (c1)/sigma chi (c1) = 0.96 +/- 0.27(s
tat) +/- 0.11(syst) for events with p(T)(J/Psi) > 4.0 GeV/c, /eta (J/Psi)/
< 0.6, and p(T)(gamma) > 1.0 GeV/c.