  We measure the mass difference, \Delta m_0, between the D*(2010)+ and the D0
and the natural line width, \Gamma, of the transition D*(2010)+ -> D0 pi+. The
data were recorded with the BABAR detector at center-of-mass energies at and
near the Upsilon(4S) resonance, and correspond to an integrated luminosity of
approximately 477 1/fb. The D0 is reconstructed in the decay modes D0 -> K- pi+
and D0 -> K- pi+ pi- pi+. For the decay mode D0 -> K- pi+ we obtain Gamma =
(83.4 +- 1.7 +- 1.5) keV and \Delta m_0 = (145 425.6 +- 0.6 +- 1.8) keV, where
the quoted errors are statistical and systematic, respectively. For the D0 ->
K- pi+ pi- pi+ mode we obtain \Gamma = (83.2 +- 1.5 +- 2.6) keV and \Delta m_0
= (145 426.6 +- 0.5 +- 2.0) keV. The combined measurements yield \Gamma = (83.3
+- 1.2 +- 1.4) keV and \Delta m_0 = (145 425.9 +- 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.
