We use 772 x 10(6) B (B) over bar meson pairs collected at the gamma(4S) resonance with the Belle detector to measure the branching fraction for (B) over bar -> X-s gamma Our measurement uses a sum-of-exclusives approach in which 38 of the hadronic final states with strangeness equal to +1, denoted by X-s, are reconstructed. The inclusive branching fraction for M-Xs < 2.8 GeV/c(2), which corresponds to a minimum photon energy of 1.9 GeV, is measured to be B(<(B)over bar> -> X-s gamma) = (3.51 +/- 0.17 +/- 0.33) x 10(-4), where the first uncertainty is statistical and the second is systematic.