We report an observation of the B±→ J/ψηK± and B0 → J/ψηK0S decays using 772 × 106BB¯ pairs collected at the γ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. We obtain the branching fractions B(B?→ J/ψηK±) = (1.27 ±0.11(stat.) ±0.11(syst.)) ×10-4 and B(B0 → J/ψηK0 S ) = (5.22 ±0.78(stat.) ± 0.49(syst.)) ×10-5. We search for a new narrow charmonium(-like) state X in the J/ψη mass spectrum and find no significant excess. We set upper limits on the product of branching fractions, B(B±→ X K± )B(X → J/ψη), at 3872MeVc-2 where aC-odd partner of X(3872) may exist, at ψ(4040) and ψ(4160) assuming their known mass and width, and over a range from 3.8 to 4.8 GeV c-2. The obtained upper limits at 90% confidence level for XC-odd(3872), ψ(4040), and ψ(4160) are 3.8 ×10-6, 15.5 ×10-6, and 7.4 ×10-6, respectively.