We present a measurement of the branching fraction and time-dependent CP violation parameters in B-0 -> a(1)(+/-)(1260)pi(-/+) decays. The results are obtained from the final data sample containing 772 x 10(6) B (B) over bar pairs collected at the Gamma(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. We obtain the product branching fraction B(B-0 -> a(1)(+/-)(1260)pi(-/+)) x B(a(1)(+/-)(1260) -> pi(+/-)pi(-/+)pi(+/-)) = (11.1 +/- 1.0(stat) +/- 1.4(syst)) x 10(-6) and an upper limit on the product branching fraction for a possible decay with the same final state B(B-0 -> a(2)(+/-)(1320)pi(-/+)) x B(a(2)(+/-)(1320) -> pi(+/-)pi(-/+)pi(+/-)) <2.2x10(-6) at 90% CL. In a time-dependent measurement to extract CP asymmetries, we obtain the CP violation parameters A(CP) = -0.06 x 0.05(stat) +/- 0.07(syst), C-CP = -0.01 +/- 0.11(stat) +/- 0.09(syst), S-CP = -0.51 +/- 0.14(stat) +/- 0.08(syst), representing time-and flavor-integrated direct, flavor-dependent direct and mixing-induced CP violation, respectively. Simultaneously, we also extract the CP-conserving parameters Delta C = +0.54 +/- 0.11(stat) +/- 0.07(syst), Delta S = -0.09 +/- 0.14(stat) +/- 0.06(syst), which, respectively, describe a rate difference and strong phase difference between the decay channels where the a(1)(+/-) does not contain the spectator quark and those where it does. We find first evidence of mixing-induced CP violation in B-0 -> a(1)(+/-)(1260)pi(-/+) decays with 3.1 sigma significance. The rate where the a(1)(+/-) 1 does not contain the spectator quark from the B meson is found to dominate the rate where it does at the 4.1 sigma level. However, there is no evidence for either time-and flavor-integrated direct CP violation or flavor-dependent direct CP violation.