We search for the Z_1(4050)^+ and Z_2(4250)^+ states, reported by the Belle Collaboration, decaying to χ_(c1)π^+ in the decays B̅ ^0→χ_(c1)K^-π^+ and B^+→χ_(c1)K_S^0π^+ where χ_(c1)→J/ψγ. The data were collected with the BABAR detector at the SLAC PEP-II asymmetric-energy e^+e^- collider operating at center-of-mass energy 10.58 GeV, and correspond to an integrated luminosity of 429 fb^(-1). In this analysis, we model the background-subtracted, efficiency-corrected χ_(c1)π^+ mass distribution using the Kπ mass distribution and the corresponding normalized Kπ Legendre-polynomial moments, and then test the need for the inclusion of resonant structures in the description of the χ_(c1)π^+ mass distribution. No evidence is found for the Z_1(4050)^+ and Z_2(4250)^+ resonances, and 90% confidence level upper limits on the branching fractions are reported for the corresponding B-meson decay modes
