Observation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">B</mml:mi><mml:mi/><mml:mo>→</mml:mo><mml:mi/><mml:mi mathvariant="italic">J</mml:mi><mml:mi>/</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">ψ</mml:mi><mml:mi mathvariant="italic">K</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>(</mml:mo><mml:mn>1270</mml:mn><mml:mo>)</mml:mo></mml:math>

We report the first observation of the exclusive decay process B-->J/psi K(1)(1270) using a sample of 11.2M BB macro meson pairs collected in the Belle detector at the KEKB asymmetric energy e(+)e(-) collider. We measure branching fractions of B[B(0)-->J/psi K(0)(1)(1270)] = (1.30+/-0.34+/-0.32) x 10(-3) and B[B(+)-->J/psi K(+)(1)(1270)] = (1.80+/-0.34+/-0.39) x 10(-3), where the first error is statistical and the second is systematic. These modes constitute approximately 15% of the total number of B-->J/psi X decays. No evidence is seen for B-->J/psi K(1)(1400) and we set an upper limit for this branching fraction.