A search is presented for the two-body charmed baryonic decays, B¯(s)0→Λc+Λ¯c-, using a data sample collected by the LHCb experiment during 2011-2012 and 2015-2018, corresponding to an integrated luminosity of 9 fb-1. The first observation of the B¯s0→Λc+Λ¯c- decay is reported with 6.2σ significance along with 4.3σ evidence for the B¯0→Λc+Λ¯c- decay. The branching fractions are measured to be B(B¯0→Λc+Λ¯c-)=(1.01-0.28+0.27±0.08±0.15)×10-5 and B(B¯s0→Λc+Λ¯c-)=(5.0±1.3±0.5±0.8)×10-5, where the first uncertainty is statistical, the second systematic, and the third due to external inputs. These results provide novel experimental inputs for the theoretical framework describing two-body baryonic decays of B mesons via W-emission and W-exchange mechanisms.