The reaction gamma p-->pi(+)K(-)K(+)n was studied at Jefferson Laboratory using a tagged photon beam with an energy range of 3-5.47 GeV. A narrow baryon state with strangeness S=+1 and mass M=1555+/-10 MeV/c(2) was observed in the nK(+) invariant mass spectrum. The peak's width is consistent with the CLAS resolution (FWHM=26 MeV/c(2)), and its statistical significance is (7.8+/-1.0)sigma. A baryon with positive strangeness has exotic structure and cannot be described in the framework of the naive constituent quark model. The mass of the observed state is consistent with the mass predicted by the chiral soliton model for the Theta(+) baryon. In addition, the pK(+) invariant mass distribution was analyzed in the reaction gamma p-->K(-)K(+)p with high statistics in search of doubly charged exotic baryon states. No resonance structures were found in this spectrum.