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We report the observation of the $B$ meson decay $B^\pm\to J/\psi \eta K^\pm$ and evidence for the decay $B^0\to J/\psi \eta K^0_S$, using {90} million $BBbar$ events collected at the $\ensuremath{\Upsilon{(4S)}}\xspace$ resonance with the $BaBar$ detector at the PEP-II $e^+ e^-$ asymmetric-energy storage ring. We obtain branching fractions of $\cal{B}$$(B^\pm\to …