In e(+)e(-) collisions recorded using the CLEO II.V detector we have studied the Cabibbo suppressed decay of D-0 ->pi(+)pi(-)pi(0) with the initial flavor of the D-0 tagged by the decay D*+-> D-0 pi(+). We use the Dalitz-plot analysis technique to measure the resonant substructure in this final state and observe rho pi and nonresonant contributions by fitting for their amplitudes and relative phases. We describe the pi pi S wave with a K-matrix formalism and limit this contribution to the rate to be < 2.5%@95% confidence level, in contrast to the large rate observed in D+->pi(+)pi(-)pi(+) decay. Using the amplitudes and phases from this analysis, we calculate an integrated CP asymmetry of 0.01(-0.07)(+0.09)+/- 0.05.
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