A search for CP violation in the decay Λb 0 → pK−μ+μ− is presented. This decay is mediated by flavour-changing neutral-current transitions in the Standard Model and is potentially sensitive to new sources of CP violation. The study is based on a data sample of proton-proton collisions recorded with the LHCb experiment, corresponding to an integrated luminosity of 3 fb−1. The Λb 0 → pK−μ+μ− decay is observed for the first time, and two observables that are sensitive to different manifestations of CP violation are measured, (Formula Presented.)where the latter is based on asymmetries in the angle between the μ+μ− and pK− decay planes. These are measured to be(Formula Presented.)and no evidence for CP violation is found.[Figure not available: see fulltext.].