  We measure the cross section for e^+e^- -> \psi(3770) -> hadrons at Ecm=3773
MeV to be (6.38+-0.08^{+0.41}_{-0.30}) nb using the CLEO detector at the CESR
e^+e^- collider. The difference between this and the e^+e^- -> \psi(3770) ->
DD-bar cross section at the same energy is found to be
(-0.01+-0.08^{+0.41}_{-0.30}) nb. With the observed total cross section, we
extract \Gamma_ee(\psi(3770))=(0.204+-0.003^{+0.041}_{-0.027}) keV.
Uncertainties shown are statistical and systematic, respectively.
