The first observation of the ¯¯¯ B 0 → J / ψ K + K − decay is presented with a data sample corresponding to an integrated luminosity of 1.0     fb − 1 of p p collisions at a center-of-mass energy of 7 TeV collected with the LHCb detector. The branching fraction is measured to be B ( ¯¯¯ B 0 → J / ψ K + K − ) = ( 2.53 ± 0.31 ± 0.19 ) × 10 − 6 , where the first uncertainty is statistical and the second is systematic. An amplitude analysis of the final state in the ¯¯¯ B 0 → J / ψ K + K − decay is performed to separate resonant and nonresonant contributions in the K + K − spectrum. Evidence of the a 0 ( 980 ) resonance is reported with statistical significance of 3.9 standard deviations. The corresponding product branching fraction is measured to be B ( ¯¯¯ B 0 → J / ψ a 0 ( 980 ) , a 0 ( 980 ) → K + K − ) = ( 4.70 ± 3.31 ± 0.72 ) × 10 − 7 , yielding an upper limit of B ( ¯¯¯ B 0 → J / ψ a 0 ( 980 ) , a 0 ( 980 ) → K + K − ) < 9.0 × 10 − 7 at 90% confidence level. No evidence of the resonant decay ¯¯¯ B 0 → J / ψ ϕ is found, and an upper limit on its branching fraction is set to be B ( ¯¯¯ B 0 → J / ψ ϕ ) < 1.9 × 10 − 7 at 90% confidence level.