Evidence is presented for the baryonic B meson decay ¯ B 0 → D 0 Λ ¯ Λ based on a data sample of 471 × 10 6 B ¯ B pairs collected with the BABAR detector at the PEP-II asymmetric e + e − collider located at the SLAC National Accelerator Laboratory. The branching fraction is determined to be B ( ¯ B 0 → D 0 Λ ¯ Λ ) = ( 9.8 + 2.9 − 2.6 ± 1.9 ) × 10 − 6 , corresponding to a significance of 3.4 standard deviations including additive systematic uncertainties. A search for the related baryonic B meson decay ¯ B 0 → D 0 Σ 0 ¯ Λ with Σ 0 → Λ γ is performed and an upper limit B ( ¯ B 0 → D 0 Σ 0 ¯ Λ + ¯ B 0 → D 0 Λ ¯ Σ 0 ) < 3.1 × 10 − 5 is determined at 90% confidence level.