We present a measurement of the branching fraction of neutral B meson decaying to final states containing a K1 meson, i.e. K{sub 1}(1270) and K{sub 1}(1400), and a charged pion. The data, collected with the BABAR detector at the Stanford Linear Accelerator Center, represent 454 million B{bar B} pairs produced in e{sup +}e{sup -} annihilation. We measure the branching fraction {Beta}(B{sup 0} {yields} K{sub 1}{sup +}{pi}{sup -}) = (31.0 {+-} 2.7 {+-} 6.9) x 10{sup -6}, where the first error quoted is statistical and the second is systematic. In the framework of the K-matrix formalism used to describe these decays, we also set limits on the ratio of the production constants for the K{sub 1}(1270){sup +} and K{sub 1}(1400){sup +} mesons in B{sup 0} decays
