We report on χc1 and χc2 production in the Feynman-x range 0.1<xF<0.8 in 515GeV/c π−Be collisions. The χc states are observed via their radiative decays into J/ψ's. The resulting photons are detected either as showers in the electromagnetic calorimeter or after conversion in the target as e+e− pairs in the tracking system. The fraction of J/ψ production due to χc1 and χc2 decays is 0.443±0.041±0.035. The ratio of the χc1 to χc2 cross section is 0.57±0.18±0.06. Our results on J/ψ, ψ(2S), and χc production indicate that 0.454±0.044±0.042 of J/ψ's are produced directly.