We report inclusive and exclusive measurements for chi(c1) and chi(c2) production in B decays. We measure B(B -> chi X-c1) = (3.03 +/- 0.05 (stat) +/- 0.24(syst)) x 10(-3) and B(B -> chi X-c2) = (0.70 +/- 0.06 (stat) +/- 0.10(syst)) x 10(-3). For the first time, chi(c2) production in exclusive B decays in the modes B-0 -> chi(c2) pi K--(+) and B-0 -> chi(c2) pi(-)pi K-+(+) has been observed, along with first evidence for the B-0 -> chi(c2) pi K--(s)0 decay mode. For chi c1 production, we report the first observation in the B+ -> chi(c1) pi(-)pi K-+(+), B-0 -> chi(c1) pi(-)pi K-+(s)0 and B-0 -> chi(c1) pi(-)pi K-+(+) decay modes. Using these decay modes, we observe a difference in the production mechanism of chi(c2) in comparison to chi(c1) in B decays. In addition, we report searches for X(3872) and chi(c1) (2P) in the B+ -> (chi(c1) pi(+)pi(-))K+ decay mode. The reported results use 772 x 10(6) B (B) over bar events collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider.