Observation of psi(3770) --> pi pi J/psi and measurement of Gamma ee[psi(2S)].

We observe signals for the decays psi(3770) --> XJ/psi from data acquired with the CLEO detector operating at the CESR e+ e- collider with square root of s = 3773 MeV. We measure the following branching fractions Beta(psi(3770) --> XJ/psi and significances: (189 +/- 20 +/- 20) x 10(-5) (11.6sigma) for X = pi+ pi-, (80 +/- 25 +/- 16) x 10(-5) (3.4sigma) for X = pi0 pi0, and (87 +/- 33 +/- 22) x 10(-5) (3.5sigma) for X = eta, where the errors are statistical and systematic, respectively. The radiative return process e+ e- --> gamma psi(2S) populates the same event sample and is used to measure Gamma ee[psi(2S)] = (2.54 +/- 0.03 +/- 0.11) keV.