Using data from proton-antiproton collisions at s√=1.96  TeV recorded by the CDF II detector at the Fermilab Tevatron, evidence for the excited resonance state Λ*0b is presented in its Λ0bπ−π+ decay followed by the Λ0b→Λ+cπ− and Λ+c→pK−π+ decays. The analysis is based on a data sample corresponding to an integrated luminosity of 9.6  fb−1 collected by an online event selection based on charged-particle tracks displaced from the proton-antiproton interaction point. The significance of the observed signal is 3.5σ. The mass of the observed state is found to be 5919.22±0.76  MeV/c2 in agreement with similar findings in proton-proton collision experiments.