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