We report the first observation of the decay Lambda(+)(c) -> pK(+)pi(-) 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(Lambda(+)(c) -> pK(+)pi(-))/B(Lambda(+)(c) -> pK(-)pi(+)) = (2.35 +/- 0.27 +/- 0.21) x 10(-3), where the uncertainties are statistical and systematic, respectively.