Observation of the decay B -> J/psi eta K and search for X(3872)-> J/psi eta

We report the observation of the B meson decay B+/--->J/psietaK(+/-) and evidence for the decay B-0-->J/psietaK(S)(0), using 90x10(6) B(B) over bar events collected at the Y(4S) resonance with the BABAR detector at the SLAC PEP-II e(+)e(-) asymmetric-energy storage ring. We obtain branching fractions of B(B+/--->J/psietaK(+/-))=[10.8+/-2.3(stat)+/-2.4(syst)]x10(-5) and B(B-0-->J/psietaK(S)(0))=[8.4+/-2.6(stat)+/-2.7(syst)]x10(-5). We search for the new narrow mass state, the X(3872), recently reported by the Belle Collaboration, in the decay B+/--->X(3872)K+/-,X(3872)-->J/psieta and determine an upper limit of B[B+/--->X(3872)K+/--->J/psietaK(+/-)]<7.7x10(-6) at 90% confidence level.