  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 $C\!P$
violation. Using data from the LHCb experiment at the Large Hadron Collider, a
search is made for $C\!P$-violating asymmetries in the decay angle
distributions of $\Lambda^0_b$ 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 $C\!P$ violation both within and beyond the
Standard Model of particle physics. We find evidence for $C\!P$ violation in
$\Lambda^0_b$ 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 $C\!P$ violation in the baryon sector.
