  We report the first search for $\bar\Lambda$--$\Lambda$ oscillations in the
decay $J/\psi \to p K^- \bar{\Lambda} + c.c.$ by analyzing $1.31\times10^9$
$J/\psi$ events accumulated with the BESIII detector at the BEPCII collider.
The $J/\psi$ events are produced using $e^+e^-$ collisions at a center of mass
energy $\sqrt{s}= 3.097$~GeV. No evidence for hyperon oscillations is observed.
The upper limit for the oscillation rate of $\bar\Lambda$ to $\Lambda$ hyperons
is determined to be $\mathcal{P}(\Lambda)=\frac{\mathcal{B}(J/\psi\to
pK^-\Lambda+c.c.)}{\mathcal{B}(J/\psi\to
pK^-\bar\Lambda+c.c.)}<4.4\times10^{-6}$ corresponding to an oscillation
parameter $\delta m_{\Lambda\bar\Lambda}$ of less than $3.8\times10^{-18}$~GeV
at the 90\% confidence level.
