  A search for baryon-number-violating $\Xi_b^0$ oscillations is performed with
a sample of $pp$ collision data recorded by the LHCb experiment, corresponding
to an integrated luminosity of 3 fb$^{-1}$. The baryon number at the moment of
production is identified by requiring that the $\Xi_b^0$ come from the decay of
a resonance $\Xi_b^{*-} \to \Xi_b^0 \pi^-$ or $\Xi_b^{\prime-} \to \Xi_b^0
\pi^-$, and the baryon number at the moment of decay is identified from the
final state using the decays $\Xi_b^0 \to \Xi_c^+ \pi^-, ~ \Xi_c^+ \to p K^-
\pi^+$. No evidence of baryon number violation is found, and an upper limit at
the 95% confidence level is set on the oscillation rate of $\omega < 0.08$
ps$^{-1}$, where $\omega$ is the associated angular frequency.
