  We present the first measurement of the D*+ width using 9/fb of e+ e- data
collected near the Upsilon(4S) resonance by the CLEO II.V detector. Our method
uses advanced tracking techniques and a reconstruction method that takes
advantage of the small vertical size of the CESR beam spot to measure the
energy release distribution from the D*+ -> D0 pi+ decay. We find Gamma(D*+) =
96 +- 4 (Statistical) +- 22 (Systematic) keV. We also measure the energy
release in the decay and compute Delta m = m(D*+) - m(D0) = 145.412 +- 0.002
(Statistical) +- 0.012 (Systematic) MeV/c^2
