Using a sample of 9.7×106 BB̄ meson pairs collected with the CLEO detector, we study B decays to the χc1 and Xc2 charmonia states, which are reconstructed via their radiative decays to J/ψ. We first measure the branching fraction for inclusive χc1 production in B decays to be B(B→χc1X) = (4.14±0.31±0.40)× 10-3, where the first uncertainty is statistical and the second one is systematic. We derive the branching fractions for direct χc1 and χc2 production in B decays by subtracting the known contribution of the decay chain B →ψ(2S)X with ψ(2S)→χc1, 2γ. We obtain B[B→χc1(direct)x] = (3.83±0.31±0.40)× 10-3. No statistically significant signal for χc2 production is observed in either case. Using the Feldman-Cousins approach, we determine the 95% confidence intervals to be [0.2, 2.0] × 10-3 for B(B→χc2X), [0.0, 1.7]× 10-3 for B[B →χc2(direct)X], and [0.00, 0.44] for the ratio Γ[B→χc2(direct)X]/Γ[B→χ c1(direct)X]. We also measure the branching ratio Γ[B→χc2(direct)X s]/Γ[B→χc1(direct)Xs] for different Xs configurations by reconstructing B decays into exclusive final states with J/ψ, γ, a kaon, and up to four pions. For all the Xs configurations, we observe a strong χc1 signal yet no statistically significant χc2 signal. We discuss how our results compare with theoretical predictions in different models of charmonium production.