  Evidence is presented for the baryonic $B$ meson decay $\bar{B}\rightarrow
D^0 \Lambda \bar{\Lambda}$ based on a data sample of $471 \times 10^6$
$B\bar{B}$ pairs collected with the {\it BABAR} detector at the PEP2 asymmetric
$e^+e^-$ collider located at the SLAC National Accelerator Laboratory. The
branching fraction is determined to be $\mathcal{B}(\bar{B}\rightarrow D^0
\Lambda \bar{\Lambda}) = (9.8^{+2.9}_{-2.6} \pm 1.9)\times 10^{-6}$,
corresponding to a significance of $3.4$ standard deviations including
systematic uncertainties. A search for the related baryonic $B$ meson decay
$\bar{B}\rightarrow D^0 \Sigma^0 \bar{\Lambda}$ with
$\Sigma^0\rightarrow\Lambda\gamma$ is performed and an upper limit
$\mathcal{B}(\bar{B}\rightarrow D^0 \Sigma^0 \bar{\Lambda} + \bar{B}\rightarrow
D^0 \Lambda \bar{\Sigma}^0) < 3.1 \times 10^{-5}$ is determined at $90\%$
confidence level.
