  We have used a study of the process e+e- --> mu+ mu- gamma at a
center-of-mass energy near the Y(4S) resonance for a mu+ mu- invariant mass
range near the J/psi mass to extract the cross section sigma(e+e- --> J/psi
gamma --> mu+ mu- gamma). The data set, corresponding to an integrated
luminosity of 88.4 fb-1, was collected using the BaBar detector at the PEP-II
collider. We measure the product Gamma(J/psi --> e+e-)B(J/psi --> mu+ mu-) to
be 0.330 +/- 0.008(stat) +/- 0.007(syst) keV. Using the world averages for
B(J/psi --> mu+ mu-) and B(J/psi --> e+e-), we derive the J/psi electronic and
total widths: Gamma(J/psi --> e+e-)=5.61+/-0.20 keV and Gamma=94.7+/-4.4 keV.
