We measure the mass difference, Δm0, between the D *(2010)+ and the D0 and the natural linewidth, Γ, of the transition D*(2010)+→D0π +. The data were recorded with the BABAR detector at center-of-mass energies at and near the Υ(4S) resonance, and correspond to an integrated luminosity of approximately 477 fb-1. The D0 is reconstructed in the decay modes D0→K-π+ and D0→K -π+π-π+. For the decay mode D0→K-π+ we obtain Γ=(83.4±1. 7±1.5) keV and Δm0=(145425.6±0.6±1.8) keV, where the quoted errors are statistical and systematic, respectively. For the D0→K-π+π-π+ mode we obtain Γ=(83.2±1.5±2.6) keV and Δm0= (145426.6±0.5±2.0) keV. The combined measurements yield Γ=(83.3±1.2±1.4) keV and Δm0=(145425. 9±0.4±1.7) keV; the width is a factor of approximately 12 times more precise than the previous value, while the mass difference is a factor of approximately 6 times more precise. © 2013 American Physical Society.