  We present measurements of the branching fractions for the decays B+/- -->
a1(1260)+/- pi0 and B+/- --> a1(1260)0 pi+/- from a data sample of 232 * 10^6
BB pairs produced in e+e- annihilation through the Y(4S) resonance. We measure
the branching fraction B(B+/- --> a1(1260)+/- pi0) * B(a1(1260)+/- --> pi- pi+
pi+/-) = (13.2 +/- 2.7 +/- 2.1) * 10^-6 with a significance of 4.2 sigma, and
the branching fraction B(B+/- --> a1(1260)0 pi+/-) * B(a1(1260)0 --> pi- pi+
pi0) = (20.4 +/- 4.7 +/- 3.4) * 10^-6 with a significance of 3.8 sigma, where
the first error quoted is statistical and the second is systematic.
