We report measurements of direct CP—violating asymmetries in charmless decays of neutral bottom hadrons to pairs of charged hadrons with the upgraded Collider Detector at the Fermilab Tevatron. Using a data sample corresponding to 1  fb−1 of integrated luminosity, we obtain the first measurements of direct CP violation in bottom strange mesons, ACP(B0s→K−π+)=+0.39±0.15(stat)±0.08(syst), and bottom baryons, ACP(Λ0b→pπ−)=+0.03±0.17(stat)±0.05(syst) and ACP(Λ0b→pK−)=+0.37±0.17(stat)±0.03(syst). In addition, we measure CP violation in B0→K+π− decays with 3.5σ significance, ACP(B0→K+π−)=−0.086±0.023(stat)±0.009(syst), in agreement with the current world average. Measurements of branching fractions of B0s→K+K− and B0→π+π− decays are also updated.