Study of B→X(3872)K, with X(3872)→J/ψπ+π-

We present measurements of the decays B+-> X(3872)K+ and B-0 -> X(3872)K-0 with X(3872) -> J/psi pi(+)pi(-). The data sample used, collected with the BABAR detector at the PEP-II e(+)e(-) asymmetric-energy storage ring, corresponds to 455x10(6)B (B) over bar pairs. Branching fraction measurements of B(B+-> X(3872)K+) x B(X(3872) -> J/psi pi(+)pi) = (8.4 +/- 1.5 +/- 0.7) x 10(-6) and B(B-0 -> X(3872)K-0) x B(X(3872) -> J/psi pi(+)pi) = (3.5 +/- 1.9 +/- 0.4) x 10(-6) are obtained. We set an upper limit on the natural width of the X(3872) of Gamma < 3.3 MeV/c(2) at the 90% confidence level.