A search for CP violation in Λb0→pK− and Λb0→pπ− decays is presented using a sample of pp collisions collected with the LHCb detector and corresponding to an integrated luminosity of 3.0fb−1. The CP -violating asymmetries are measured to be ACPpK−=−0.020±0.013±0.019 and ACPpπ−=−0.035±0.017±0.020, and their difference ACPpK−−ACPpπ−=0.014±0.022±0.010, where the first uncertainties are statistical and the second systematic. These are the most precise measurements of such asymmetries to date.