We report the observation of the decay mode B(+/-) --> p(-)pK(+/-)based on an analysis of 29.4 fb(-1) of data collected by the Belle detector at KEKB. This is the first example of a b-->s transition with baryons in the final state. The p(-)p mass spectrum in this decay is inconsistent with phase space and is peaked at low mass. The branching fraction for this decay is measured to be B(B+/--->p(-)pK+/-) = [4.3(+1.1)(-0.9)(stat)+/-0.5(syst)]x 10(-6). We also report upper limits for the decays B(0)-->p(-)pK(S) and B(+/-)-->p(-)p pi(+/-).