We present measurements of the branching fractions for the decays B;{+/-}-->a_{1};{+/-}(1260)pi;{0} and B;{+/-}-->a_{1};{0}(1260)pi;{+/-} from a data sample of 232x10;{6} BB[over ] pairs produced in e;{+}e;{-} annihilation through the Upsilon(4S) resonance. We measure the branching fraction B(B;{+/-}-->a_{1};{+/-}(1260)pi;{0})xB(a_{1};{+/-}(1260)-->pi;{-}pi;{+}pi;{+/-})=(13.2+/-2.7+/-2.1)x10;{-6} with a significance of 4.2sigma, and the branching fraction B(B;{+/-}-->a_{1};{0}(1260)pi;{+/-})xB(a_{1};{0}(1260)-->pi;{-}pi;{+}pi;{0})=(20.4+/-4.7+/-3.4)x10;{-6} with a significance of 3.8sigma, where the first error quoted is statistical and the second is systematic.