First observations of the Cabibbo-suppressed decays B(0) → D(+)K(-)π(+)π(-) and B(-) → D(0)K(-)π(+)π(-) are reported using 35 pb(-1) of data collected with the LHCb detector. Their branching fractions are measured with respect to the corresponding Cabibbo-favored decays, from which we obtain B(B(0) → D(+)K(-)π(+)π(-))/B(B(0) → D(+)π(-)π(+)π(-))=(5.9±1.1±0.5)×10(-2) and B(B(-) → D(0)K(-)π(+)π(-))/B(B(-) → D(0)π(-)π(+)π(-))=(9.4±1.3±0.9)×10(-2), where the uncertainties are statistical and systematic, respectively. The B(-) → D(0)K(-)π(+)π(-) decay is particularly interesting, as it can be used in a similar way to B(-) → D(0)K(-) to measure the Cabibbo-Kobayashi-Maskawa phase γ.