Measurement of sigma(e^+e^- --> psi(3770) --> hadrons) at E_(cm)=3773 MeV

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.