We report the first observation of the Xi _{c}(2930)^0 charmed-strange baryon with a significance greater than 5sigma . The Xi _{c}(2930)^0 is found in its decay to K^- Lambda _{c}^+ in B^{-} rightarrow K^{-} Lambda _{c}^{+} bar{Lambda }_{c}^{-} decays. The measured mass and width are [2928.9 pm 3.0(mathrm stat.)^{+0.9}_{-12.0}(mathrm syst.)] MeV/c^{2} and [19.5 pm 8.4(mathrm stat.) ^{+5.9}_{-7.9}(mathrm syst.)] MeV, respectively, and the product branching fraction is mathcal{B}(B^{-} rightarrow Xi _{c}(2930)^0 bar{Lambda }_{c}^{-}) mathcal{B}(Xi _{c}(2930)^0 rightarrow K^- Lambda _{c}^{+})=[1.73 pm 0.45(mathrm stat.) pm 0.21(mathrm syst.)]times 10^{-4}. We also measure mathcal{B}(B^{-} rightarrow K^{-} Lambda _{c}^{+} bar{Lambda }_{c}^{-}) = [4.80 pm 0.43(mathrm stat.) pm 0.60(mathrm syst.)] times 10^{-4} with improved precision, and search for the charmonium-like state Y(4660) and its spin partner, Y_{eta }, in the Lambda _{c}^{+}bar{Lambda }_{c}^{-} invariant mass spectrum. No clear signals of the Y(4660) nor its spin partner are observed and the 90% credibility level (C.L.) upper limits on their production rates are determined. These measurements are obtained from a sample of (772pm 11)times 10^{6} Bbar{B} pairs collected at the Upsilon (4S) resonance by the Belle detector at the KEKB asymmetric energy electron–positron collider.