We present the first observation of the baryon decay Λ0b→Λ+cπ− followed by Λ+c→pK−π+ in 106  pb−1 pp collisions at s√=1.96  TeV in the CDF experiment. In order to reduce systematic error, the measured rate for Λ0b decay is normalized to the kinematically similar meson decay B0→D+π− followed by D+→π+K−π+. We report the ratio of production cross sections (σ) times the ratio of branching fractions (B) for the momentum region integrated above pT>6  GeV/c and pseudorapidity range |η|<1.3: σ(pp→Λ0bX)/σ(pp→B0X)×B(Λ0b→Λ+cπ−)/B(B0→D+π−)=0.82±0.08(stat)±0.11(syst)±0.22[B(Λ+c→pK−π+)].