A search for the B-0 -> K+K- decay is performed using pp-collision data collected by LHCb. The data set corresponds to integrated luminosities of 1.0 and 2.0 fb(-1) at center-of-mass energies of 7 and 8 TeV, respectively. This decay is observed for the first time, with a significance of more than 5 standard deviations. The analysis also results in an improved measurement of the branching fraction for the B-s(0) -> pi(+)pi(-) decay. The measured branching fractions are B(B-0 -> K+K-) = (7.80 +/- 1.27 +/- 0.81 +/- 0.21) x 10(-8) and B(B-s(0) -> pi(+)p(-)) = (6.91 +/- 0.54 +/- 0.63 +/- 0.19 +/- 0.40) x 10(-7). The first uncertainty is statistical, the second is systematic, the third is due to the uncertainty on the B-0 -> K+pi(-) branching fraction used as a normalization. For the B-s(0) mode, the fourth accounts for the uncertainty on the ratio of the probabilities for b quarks to hadronize into B-s(0) and B-0 mesons.