We present the first observation of the baryon decay Lambda b0-->Lambda c+pi- followed by Lambda c+-->pK-pi+ in 106 pb-1 pp collisions at square root s=1.96 TeV in the CDF experiment. In order to reduce systematic error, the measured rate for Lambda b0 decay is normalized to the kinematically similar meson decay B0-->D+pi- followed by D+-->pi+K-pi+. We report the ratio of production cross sections (sigma) times the ratio of branching fractions (B) for the momentum region integrated above pT>6 GeV/c and pseudorapidity range |eta|<1.3: sigma(pp-->Lambda b0X)/sigma(pp-->B0X)xB(Lambda b0-->Lambda c+pi-)/B(B0-->D+pi-)=0.82+/-0.08(stat)+/-0.11(syst)+/-0.22[B(Lambda c+-->pK-pi+)].