We search for decays of the type B0(s)→h+h'− (where h,h′=K or π) in 180  pb−1 of pp collisions collected at the Tevatron by the upgraded Collider Detector at Fermilab. We report the first observation of the new mode B0s→K+K− with a yield of 236±32 events, corresponding to (fs/fd)×B(B0s→K+K−)/B(B0→K+π−)=0.46±0.08(stat)±0.07(syst), where fs/fd is the ratio of production fractions of B0s and B0. We find results in agreement with world averages for the B0 modes, and set the following new limits at 90% C.L.: B(B0s→K−π+)<5.6×10−6 and B(B0s→π+π−)<1.7×10−6.