Dalitz Analysis of D^0 --> K_S^0 pi+ pi-

In e^+ e^- collisions using the CLEO detector we have studied the decay of the D^0 to the final state K_S^0 pi^+ pi^- with the initial flavor of the $D^0$ tagged in charged D^* decay. We use the Dalitz technique to measure the resonant substructure in this final state and clearly observe ten different contributions by fitting for their amplitudes and relative phases. We observe a K^{* +} pi^- component which arises from doubly Cabibbo suppressed decays or D^ 0- bar{D^0} mixing.