Observation of B+ --> a1+(1260) K0 and B0 --> a1-(1260) K+

We present branching fraction measurements of the decays B(+)-->a(1)(+)(1260)K(0) and B(0)-->a(1)(-)(1260)K(+) with a(1)(+/-)(1260)-->pi(-/+)pi(+/-)pi(+/-). The data sample corresponds to 383 x 10(6) BB pairs produced in e(+)e(-) annihilation through the Upsilon(4S) resonance. We measure the products of the branching fractions B(B(+)-->a(1)(+)(1260)K(0)B(a(1)(+)(1260)-->pi(-)pi(+)pi(+))=(17.4+/-2.5+/-2.2) x 10(-6) and B(B(0)-->a(1)(-)(1260)K(+)B(a(1)(-)(1260)-->pi(+)pi(-)pi(-)) = (8.2+/-1.5+/-1.2) x 10(-6). We also measure the charge asymmetries A(ch)(B(+)-->a(1)(+)(1260)K(0) = 0.12+/-0.11+/-0.02 and A(ch)(B(0)-->a(1)(-)(1260)K+) = -0.16+/-0.12+/-0.01. The first uncertainty quoted is statistical and the second is systematic.