Differences in the behaviour of matter and antimatter have been observed in K and B meson decays, but not yet in any baryon decay. Such differences are associated with the non-invariance of fundamental interactions under the combined charge-conjugation and parity transformations, known as CP violation. Here, using data from the LHCb experiment at the Large Hadron Collider, we search for CP-violating asymmetries in the decay angle distributions of $\Lambda_b^0$ baryons decaying to $p\pi^-\pi^+\pi^-$ and $p\pi^-K^+K^-$ final states. These four-body hadronic decays are a promising place to search for sources of CP violation both within and beyond the standard model of particle physics. We find evidence for CP violation in $\Lambda_b^0$ to $p\pi^-\pi^+\pi^-$ decays with a statistical significance corresponding to 3.3 standard deviations including systematic uncertainties. This represents the first evidence for CP violation in the baryon sector.