We search for new charmless decays of neutral b hadrons to pairs of charged hadrons, using 1 fb(-1) of data collected by the CDF II detector at the Fermilab Tevatron. We report the first observation of the Bs0-->K-pi+ decay and measure B(Bs0-->K-pi+)=(5.0+/-0.7(stat)+/-0.8(syst))x10(-6). We also report the first observation of charmless b-baryon decays, and measure B(Lambdab0-->ppi-)=(3.5+/-0.6(stat)+/-0.9(syst))x10(-6) and B(Lambdab0-->pK-)=(5.6+/-0.8(stat)+/-1.5(syst))x10(-6). No evidence is found for other modes, and we set the limit B(Bs0-->pi+pi;-)<1.2x10(-6) at 90% C.L.