A study of the B +→ J / ψ Λ ¯ p decay using proton-proton collision data collected at s = 8 TeV by the CMS experiment at the LHC, corresponding to an integrated luminosity of 19.6 fb−1, is presented. The ratio of branching fractions B(B+→J/ψΛ¯p)/B(B+→J/ψK∗(892)+) is measured to be (1.054 ± 0.057(stat) ± 0.035(syst) ± 0.011(B))%, where the last uncertainty reflects the uncertainties in the world-average branching fractions of Λ ¯ and K*(892) + decays to reconstructed final states. The invariant mass distributions of the J / ψ Λ ¯ , J/ψp, and Λ ¯ p systems produced in the B +→ J / ψ Λ¯ p decay are investigated and found to be inconsistent with the pure phase space hypothesis. The analysis is extended by using a model-independent angular amplitude analysis, which shows that the observed invariant mass distributions are consistent with the contributions from excited kaons decaying to the Λ ¯ p system. [Figure not available: see fulltext.]