We search for annihilation decay modes of neutral b mesons into pairs of charmless charged hadrons with the upgraded Collider Detector at the Fermilab Tevatron. Using a data sample corresponding to 6 fb(-1) of integrated luminosity, we obtain the first evidence for the B-s(0) -> pi(+)pi(-) decay, with a significance of 3.7 sigma, and a measured branching ratio B(B-s(0) -> pi(+)pi(-)) = (0.57 +/- 0.15(stat) +/- 0.10(syst)) x 10(-6). A search for the B-0 -> K+K- mode in the same sample yields a significance of 2.0 sigma, and a central value estimate B(B-0 -> K+K-) = (0.23 +/- 0.10(stat) +/- 0.10(syst)) x 10(-6).
