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) B (B) over bar pairs produced in e(+)e(-) annihilation through the Y(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 +/- 001. The first uncertainty quoted is statistical and the second is systematic.