  We have observed the rare decay B0 => rho+ rho- in a sample of 89 million BB
pairs recorded with the BABAR detector. The number of observed events is 88
+23-21 +-9, with a significance of 5.1 standard deviations with systematic
uncertainties included. The branching fraction and the longitudinal
polarization are measured to be BR(B0 => rho+ rho-) = (25 +7-6 +5-6)*10^{-6}
and Gamma_L/Gamma = 0.98 +0.02-0.08 +-0.03, respectively.
