The cross section for e(+)e(-) --> rho pi has been measured by the BES
detector at BEPC at center-of-mass energies covering a 40 MeV interva
l spanning the J/psi resonance. The data are used to search for the ve
ctor gluonium state hypothesized by Brodsky, Lepage, and Tuan as an ex
planation of the rho pi puzzle in charmonium physics. The shape of the
rho pi cross section is compatible with that of the total hadronic cr
oss section. No distortions indicating the presence of a vector glueba
ll are seen.