We perform the first measurement on the D 0 − ¯ D 0 mixing parameters using a time-dependent amplitude analysis of the decay D 0 → π + π − π 0 . The data were recorded with the BABAR detector at center-of-mass energies at and near the Υ ( 4 S ) resonance, and correspond to an integrated luminosity of approximately 468.1     fb − 1 . The neutral D meson candidates are selected from D ∗ ( 2010 ) + → D 0 π + s decays where the flavor at the production is identified by the charge of the low-momentum pion, π + s . The measured mixing parameters are x = ( 1.5 ± 1.2 ± 0.6 ) % and y = ( 0.2 ± 0.9 ± 0.5 ) % , where the quoted uncertainties are statistical and systematic, respectively.