We present evidence of D[superscript 0]-D̅[superscript 0] mixing using a time-dependent amplitude analysis of the decay D0→K[superscript +]π[superscript -]π[superscript 0] in a data sample of 384 fb[superscript -1] collected with the BABAR detector at the PEP-II e[superscript +]e[superscript -] collider at the Stanford Linear Accelerator Center. Assuming CP conservation, we measure the mixing parameters x[subscript Kππ][superscript 0′]=[2.61[subscript -0.68] [superscript +0.57](stat)±0.39(syst)]%, y[subscript Kππ][superscript 0′]=[-0.06[subscript -0.64][superscript +0.55](stat)±0.34(syst)]%. This result is inconsistent with the no-mixing hypothesis with a significance of 3.2 standard deviations. We find no evidence of CP violation in mixing. Science and Technology Facilities Council, United Kingdom MEC (Spain) MES (Russia) NFR (Norway) FOM of the Netherlands Istituto Nazionale di Fisica Nucleare of Italy DFG (Germany) Bundesministerium für Bildung und Forschung, Germany CNRS-IN2P3 (France) CEA (France) Natural Sciences and Engineering Research Council of Canada National Science Foundation Department of Energy