We have observed the rare decay B-0-->rho(+)rho(-) in a sample of 89 million B (b) over bar pairs recorded with the BABAR detector. The number of observed events is 88(-21)(+23)+/-9, with a significance of 5.1 standard deviations with systematic uncertainties included. The branching fraction and the longitudinal polarization are measured to be B(B-0-->rho(+)rho(-))=(25(-6-6)(+7+5))x10(-6) and Gamma(L)/Gamma=0.98(-0.08)(+0.02)+/-0.03, respectively.
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