We report the first observation of the decay Λ_{c}^{+}→pK^{+}π^{-} using a 980 fb^{-1} data sample collected by the Belle detector at the KEKB asymmetric-energy e^{+}e^{-} collider. This is the first observation of a doubly Cabibbo-suppressed decay of a charmed baryon. We measure the branching ratio of this decay with respect to its Cabibbo-favored counterpart to be B(Λ_{c}^{+}→pK^{+}π^{-})/B(Λ_{c}^{+}→pK^{-}π^{+})=(2.35±0.27±0.21)×10^{-3}, where the uncertainties are statistical and systematic, respectively.